You can get beds in Havana legally for well under 10CUC just look for Casa d' Mochilero (last time I had somebody sleeping there was 5CUC/person) or similar ones like these:
https://www.absolutviajes.com/tres-albergues-juveniles-para-mochileros-en-la-habana/
And yes, some are very well placed. To save money in Havana start reading on what are the almendrones and how they work, it;s a kind of shared taxi. City buses are much more efficient nowadays than what most guidebooks make them look like, particularly if you are staying anywhere near Coppelia.

Food can be very cheap in Cuba, you can easily get a lunch under 1$, but don't expect it to be gourmet. Some street snacks are filling and don't taste too bad. Nightlife can be very cheap as well; most fun is on the street and it's easy to find, cinema and theater are also cheap, even for foreigners and if your Spanish is good theater in Cuba is full of political hints and gives a GREAT insight into everyday life.

Intercity transport will be a pain in the ass for your budget, forget about hitchhiking for free. Sharing taxis is the way to go and casa owners -particularly outside Havana- can arrange that for you (expect a 5CUC commission...).

It's a personal thing, but I would not spend too much beach time in Cuba. Beaches are not as good as where I come from (they'r not bad, just nothing to write home about), getting there is time consuming and some of the best ones are only for the all-inclusive crowds or those who don't mind being around them. I'd stick to the beaches east of Havana which are rife with Cuban life, easy to get to and offer some glimpse into real Cuban life, Santa Maria and Boca Ciega being the best of the bunch.

As far as your plan goes:
-Havana 3
- Vinales 3
-Varadero 0
-Cayo Largo 0 (VERY expensive to get to)
-Trinidad-Cienfuegos (2 Trinidad, 1 Cienfuegos)
-Cayo las Brujas 0
-Cayo Guillermo 0
-Camaguey 2
-Santiago 2
-Baracoa 3

This way you have 16 days. I'd spend some time in Remedios, Gibara (the route between Baracoa and Gibara crossing Humbolt Nacional Park is a must) and I'd add a place like Banes for history, archaeology, politics and eeveryday life off the tourist trail, possibly even visit Biran.
Again, in my plan there's only beach time in Trinidad (Ancon), Baracoa (playa maguana) and Havana (Santa Maria). Doable in 20 days, people have been doing it in less. Try to get a couple of night buses; it saves time and money (you don't spend on accommodation) but have some warm clothes for the bus.

Eh - reading your post I got interested in that crossing you mentioned as I have never been there. But I know Nam Yun and some villages nearby. Now from what I understand from the sparse online data is that this crossing is similar to some Thai/Laos crossing-markets where local can do some business. It is not an official border crossing which can be used by foreigners. As stated above, this is what I understand.
The crossing in Phu Singh is in a remote spot with only hitchhiking or hired motorbikes in the past. I did it more than once and met nice people in that way. Since then the casino at the border as opened and I suspect there should be a casino van from Sisaket town running the distance up that mountain. Anyhow, if you are after seeing Khmer temples the entire region is rich and with many pickings.
Crossing to Anlong Veng is very easy. Lots of traffic to the town. Anlong Veng - Sra Em is also very easy, vans, buses, shared taxis.
Phu Singh is a very easy crossing without waits - unlike Poipet during rush hour.

I m not sure why you want to go to Nam Yun directly. There is Phimai, Phanom Rung, Ta Muam Tam (spelling), and a number of other good places to see along the way. If you just want to get quickly to Siem Reap take the bus or - i like it more - the train to the border and then on by bus.

Sorry that I m a little vague, it is just that I dont fully understand your preferences.

Title: 18 Reasons I am Determined to Overland Africa

Destinations covered: South Africa, Namibia, Botswana, Zambia, Malawi, Zimbabwe

Theme: Personal experience

Style: List format

Synopsis: Many of the Africans have no idea why we would want to travel Africa when all they want to do is travel to the US. Then there are the others who think we will spend the whole time paying bribes, hitchhiking, and taking freezing cold bucket showers…or in other words it’s their idea of hell. Many people just want to know why we are doing a self-drive through Africa. So here is my best attempt to answer why I want to travel Africa.

URL: http://theworldpursuit.com/traveling-africa/

No, rental car is not the only way to get around and on your own. You can also hire a private taxi which will be no more expensive--often less--than a rental car. Most drivers charge little or nothing to hang around and wait while you explore or spend several hours on the beach, because in Cuba, it's not time that's costly, it's gasoline. Driving distance matters more than time.

Thing is, you seem to have two different things in mind. One is to hang with the locals, and one is to get yourself a rental car and run around the area. For hanging with the locals, Gibara is a good place, being pleasant bay-front town with a pretty beach 5 or 10 km to the east (I forget how far; Candy can tell you since she lives there.) You're less likely to meet and hang with the locals if you rent a car and spend hours driving around in your air-conditioned bubble to different locals, with less time (because you've spent so much time getting there and back to your base) to spend with any locals who might be about. If you do manage to get a rental car, the best way to meet locals is to pick up hitchhikers the minute you start out anywhere. They often make good guides (better than your map) and may invite you to visit their home when you drop them off. (Just be sure not to leave anything loose lying about in the car; keep it all locked in the trunk or close at hand. I always, always pick up hitchhikers, even though I have lost a few things, including my bathing suit, a pocket knife, and misc other stuff. I still pick people up, but am careful not to tempt them they might not be able to resist.)

If you want to explore the area, then I would suggest that you might do better to base yourself in Holguin and do day or overnight trips to: Gibara, Guardalavaca, Bayamo, and Santo Domingo/the Comandancia de la Plata. The first two are an hour or less north of Holguin, on the coast. Bayamo is an hour south of Holguin, and Santo Domingo, three hours south of Holguin, up in the mountains. (You can read up on all of them in your guide book or on-line.) There are casas in all these places and you don't have to book them through airbnb. Just go to the website www.cubacasas.net or some other.

every time you head out anywhere.

I've probably racked up as many miles on trans-continental road trips as anyone else on this site. I've been doing it as a driver since the late 1960s too. I enjoy it and I don't criticize the OP for wanting to try it. I usually do it for some well defined reasons, e.g., someone is paying me or there is some specific event or site I want to participate in or see. If the OP wants to do this just to say he did it, that's OK with me.

I would offer the OP some lessons "learned the hard way:"
1. Do you have a car that is up to the trip? If you don't, don't do this. Nothing spoils a trip faster than car trouble in the middle of nowhere.
2. A random selection of "travel buddies," such as whoever PMs you first, is not a good idea. I'm sure they are all perfectly nice people, but you will be amazed easily different personalities can become intolerable to each other after they are cooped up together in a car for a week. When I do travel with others, which is rare, I am VERY PICKY about with whom I am traveling.
3. KNOW YOUR LIMITS. Be able to recognize when you are becoming fatigued, or worse, hypnotized by the drive. The only way I gained this knowledge was to gradually build up to long drives. I am certain you don't do it by jumping into a car and heading for New York. If you intend to let your randomly selected travel buddies drive any distance, simple self-preservation demands that both you and they also know their limits.
4. Have at least a rough idea of your schedule and stick to it. Otherwise, you will find yourself with too little time to drive too many miles.
5. Have a minimum list of what you want to see and be sure that all of your buddies agree to it BEFORE you start. There will be conflicts if you don't do this.
6. Take enough money, a credit card that is not maxed out will do, so that you can cover the unexpected. Being stuck in the middle of nowhere with a dead car and no money is an unmitigated disaster.
7. Have a written agreement with all of your travel buddies about how expenses will be shared.
8. Have a AAA membership.
9. Don't pick up hitchhikers.

Have a great time.

Hitchhike...

I was in Santa Elena to see the church within the last year and don't remember seeing any bicycles for rent (though I wasn't looking). I wanted to tell you that I walked and hitchhiked the Ruta Puuc on that trip...there is very little auto traffic on the road, but there are long stretches of road that have no shoulder on either side...the vegetation comes right to the pavement, and the traffic that does pass by is often going fast. If no problems, it would be a nice ride. Wishing you a safe one.