In case you want to stick to Southeast Asia, I would consider the following destinations (in random order):
Bangkok. Either fly there or travel overland from Chiang Mai to Bangkok by train (do this if you want to experience a night train journey, not for for saving a flight). On the way you could also stop for a night in one of the former capitals of Thailand, Sukothai. Bangkok is totally different to the other destinations you are looking at. Very vibrant, plenty to see, plenty to do. Not always pretty but for me one of the most interesting places on earth. Fantastic for food, for shopping, for nightlife, and also really great if you or your mother would like to enjoy massages, face treatments etc. There are also several wonderful temples there, you can enjoy the city from the water by taking the Chao Prya river buses, there is the very lively Chatuchak market etc. etc. etc.

Penang, Malaysia. Georgetown, the "capital" of Penang is a wonderful city with a great mix of Malay, Indian, Chinese and Western culture, architecture, religion and food. I especially love Penang for this great mix, and for foodies like me, its really a wonderful paradise and one of my favorite places in Asia. Georgetown has many colonial buildings, interesting temples / mosques / churches, great food markets and much more. Also, on Penang you can enjoy some beach time, for example in Batu Ferrenghi (which also has a fantastic night market by the way). The beaches are not amazing, but good enough for a couple of hours to enjoy the beach and sea.

It's actually much easier to fly than travel such long distances overland. Yangon-Bangkok you're there in less than an hour, as opposed to 20-30 hours of travel overland and there are numerous cheap flights Bangkok-Chiang Mai in case Chiang Mai doesn't have a direct connection to Myanmar - which I don't know. So for most people that section overland would be too much of a pain. It probably would not be cheaper either. The weather's very hot in Asia and buses can be poor quality, so it's best if you stick to overland routes that are popular, if you want to do stuff other people aren't doing make sure it's well planned.

There will be banks open 24/7 at Suv.
Don Muang ?unknown?
Rates are comparable - no reason NOT to change money at Suv.

Very important you buy your ticket from where you board the train as if you do not get on in Bangkok they may sell your berth to someone else

This is my main concern. Sounds like the best bet will indeed be to buy a ticket from Lop Buri --> Chiang Mai, and if I change my mind Plan B can be buying a last minute ticket from Bangkok directly to Lop Buri that day.

I agree. I don't see why there should only be one international crossing at any given point, when there's enough traffic to justify multiple crossings.

Between other countries like the USA and Mexico, there are often 3-4 crossings between each city pair, not just one. And to the best of my knowledge most of these allow foreigners across and not just locals.

However, between Thailand and Malaysia there are sometimes multiple crossings within a short distance of each other and foreigners can use all these crossings, unless they're designated only as "local" though the majority are international. Case in point is Sadao and Padang Besar. Both are relatively close to each other and both are international.

With regards to forcing foreigners to use bridges once they open instead of river crossings as is the case at the Thai-Lao border, I guess this is because the officials decided everything needs to be moved to the bridges leaving the ferry crossings only for border hopping locals. At Chiang Khong, I have used both the ferry and the bridge - the latter opened around late 2013 I think it was. The old arrangement was very inconvenient for drivers as 1) you had to pay 1000 Baht for the car ferry and 2) get your passport stamped at a location 5km away in town.
However, for passengers such as tourists it was in many ways more scenic and atmospheric as you point out.

In the specific case of Mae Sot - Myawaddy, I don't see any reason why they can't have both bridges open for all types of travellers and let us choose, which one to cross.

The new bridge won't allow pedestrians to cross - you'll be forced to get on a bus. I think bicyclists will probably be required to put their bike on a bus in order to be allowed across but this remains to be seen.

As I said, all of this is still very new and I have heard conflicting information on what will happen when it first opens. We'll just have to wait until after the bridge opens to find out what the procedures will be like.

I agree with you with respect to this occurring on Friendship Bridge 1 as cars and an increasing number of trucks have shared the narrow space on the bridge for 22 years and the crossover point in the middle is dangerous and poorly designed. Traffic is often jammed because one impatient Burmese driver decides to switch to the other side before making it to the halfway point while an oncoming vehicle is in front of him. Burmese drivers are far more impatient than even Thai drivers so this occurs pretty much everyday, especially around lunchtime when traffic volume is at it's greatest.

Traffic is also backed up on the access roads both on the Thai and Myanmar sides and large trucks really shouldn't be traveling through city streets. At night, Thai trucks are parked, blocking one lane on the Myanmar side while waiting for the border to open at 5am Myanmar time the next morning.

Of course, back in 1996 up to as late as around 2012 there was such little traffic that it didn't matter much, but in recent months and years bottlenecks have become common. Another danger has been for us tourists who have to be careful not to get squashed by cargo trucks when we enter or exit the immigration facilities on the Myanmar side as there is almost no space for pedestrians to walk.

I doubt that cargo trucks would be fast moving across these bridges though given that they have to stop for customs and immigration on both sides. In any case, the second bridge is designed for all types of vehicles - there are separate windows for drivers of vehicles and pedestrians.

Eventually a bus service will connect Mae Sot and Myawaddy and tourists will mostly be directed towards using that service, similar to crossings between Chiang Khong and Huay Xai and Mukdahan and Savannakhet.

Not long in Myanmar. I don't think you will find any direct flight to Chiang Rai or Chiang Mai even. You could look at crossing land border at Mae Sot then take a bus or maybe there is flight from there to Chiang Rai. But Mae Sot is in south near Hpa-An and Mawlamyine. So you will need to plan your route. Flying to Mandalay then boat to Bagan is better. I would probably fly into Mandalay then go to Yangon towards end. I would not spend more time in Vientiane and Savannakhet, thay are ok for 1 day each, Luang Prabang is much more interesting place and worth about 3 days.

A while ago, I posted this. You might find some interesting tips on rides and rental:
https://www.lonelyplanet.com/thorntree/forums/on-your-bike/topics/looking-for-the-ideal-one-month-ride-in-south-east-asia-fall-2018

I am a big fan of Albin_3 journals. Read them for ideas and tips.

I am currently in Dan Sai in Notrthern Thailand. Rented a good touring bike from Mong Cycle in Phrao (close to Chiang Mai): one month for 6000bahts, backrack Included. Hilly region tough. I did a two months squats and lunges routine before coming here. On my way to Chiang Khan and then Vientiane. Looking myself for idea for my last full week after that 1000km wonderful tour.
https://charlotenasie2016.wordpress.com/
Had to take a three days break to take care of a saddle sore issue. Back on the road tomorrow.

Remember, you can always include a bus or train leg to avoid too steep sections.