I would skip Vientiane and Phnom Penh in my opinion.
I found that they had very little to offer and not worth staying more than 1 day.

If you want to take it slow, highly recommend the slow boat between the city you arrive at the border at Laos from Rai to Luang Prabang. I don't know if this runs during the rainy season.

Chiang Rai is a nice stopover point before crossing the border, no need to stay there that long as there is very little to do besides the White temple (definitely worth seeing).

I think that will give you plenty of time for the other places. Just don't forget that travelling between places can take a fairly long time so try to include that in your plan.

If there are any holidays for those countries then expect delays or less transport available.

Hope this helps, if you have any questions let me know

Yes, there is plenty of it.

It generally applies at most tourist attractions and possibly some types of accommodation though this is rare. Dual pricing was abolished for domestic flights a few years back.

Unofficial dual pricing is common at markets but if you can speak the local lingo and are "street smart" it's relatively easy to avoid.

As an example, you may find places such as the Khonkapaeng waterfalls near the Cambodian border charge foreigners 55,000 Kip, while locals pay at most 20,000. The Patuxai monument in Vientiane used to charge 1,000 for locals and 3,000 for foreigners, but not sure if this has since gone up. Wat Phra That Luang, the famous symbol of Laos at the top of a short hill in Vientiane charges foreigners I think it's 5,000 Kip and 2,000 for locals. Now of course that may have since increased to 20,000 but I haven't visited in years. The Royal Palace in Luang Prabang and the famous waterfall Kuang Si also charge foreigners more than Lao citizens. Of course this is only a small selection - the majority of touristy places with an entrance fee will charge foreigners more. To hide the fact there's dual pricing, sometimes there is a Lao sign stating "Lao citizens get in for half price" or something like that.

The best combination of comfortable and fast is fly from Luang Prabang to Chiang Rai, via Bangkok, and use bus from Chiang Rai to Chiang Khong. Even though you have to change flights in Bangkok, still faster than direct buses, which would take 12+ hours on bad roads.

I ate better in Luang Prabang.

Neither of those is up there with the best in SE Asia though....

I agree that maybe cut out CR this time. There is plenty of countryside visits in the Chiang Mai province including waterfalls and Thailand's highest peak.

My initial thoughts are to avoid the "mega cities" which have a population of 2-6 million+ and go for small cities / large towns like Chiang Mai, Siem Reap, Luang Prabang, Vientiane, Hoi An etc, which all only have modest traffic and you can easily walk and ride a bicycle / scooter around. They all have a strong local culture, but also an international influence in the form of varied restaurants, bars and nightlife.

The next step is to consider which of those has the activities / cultural immersion that you are looking for.

You could also start at Mae Sariang rather than Chiang Mai then after spending time at Mae Sariang head to Mae Hong Song (just a big town these days) then proceed to Soppong (Pang Mapha) . Suggest staying at Cave Lodge at Tham Lod village 9 kms from Soppong rather than staying at Soppong. Then make your way to Chiang Mai and from there to Chiang Rai.
If not in a rush you could throw the itinerary away and wing it. July and August could be difficult time for weather . Could have on and off drenching rain most days.