So is the plan Thailand, Cambodia, Vietnam? I'm assuming Cambodia over Laos. I've been to every country in SE Asia, some several times, but not for as long as you will be travelling (at least, not at one time). I usually travel there in Feb/Mar but occasionally from July-Sept. Mar/Apr will definitely be hot and dry. There will be a lot of slash and burn over multiple countries, plus other forms of pollution, so you will have a lot of hazy skies, especially during the day. I always found that early morning (i.e. right after sunrise) and dusk/evening to be the times to photograph, not only because of the respite from the haze and heat, but because that's when the locals are out doing their thing, before (or after) they have to go to work. Like you, I don't really shoot crowded cities or people, and as such I don't really enjoy most of the cities in SE Asia. The only exception to that rule is a few Vietnamese cities that I stopped in, like Hanoi - the last I was there it still had a faded colonial charm but was very chaotic in an old-school sense. Hue and Hoi An were also nice places to be in and explore from. HCM City was too modern and boring in comparison.
I've travelled by bus, car, train, and boat through these countries. The train was an overnighter in Vietnam (Hanoi to Hue I think). If you were interested in photographing part of the aspect of train travel it could be interesting, but I'm not sure how well it would lend itself to go photos of the countryside at this time of year. My memory of it was a lot of barren fields, or of newly planted rice. A lot of people do the boat trip from Siem Reap to Phnom Penh on the Tonle Sap Lake in order to photograph the fishing villages along the shore, but the water levels may be too low at this time of year for you to do it. If you really want to photograph the countryside well, I would recommend to rent a scooter or hire a driver to take you - you'll probably have a higher success rate for photographs.
I have never really gotten off the beaten track when travelling here, for a variety of reasons, partly due to the short amount of time that I've been there, or other obligations (like conferences that take place in major cities), etc. That said, here are a few impressions I've had of the countries on your list:
Thailand
Are you sure you want to start here? I imagine the water festival in April would be a really fun event to photograph if you have some way of protecting your camera. (I realise you've probably planned it this way because of flights).
Bangkok - Even though I enjoy visiting some of the sites here, I've never really had an success in photographing it. However, some of posters here, like (there was a url link here which no longer exists), have made really interesting (street) photos while there.
Chiang Mai - I like this city more, but mostly because it's closer to things to do outside of the city. My best experience here was volunteering at
Elephant Nature Park for a week, where we got to feed and bathe and do various other chores over the week. It really wasn't that strenuous (a couple hours in the morning, then a couple more in the afternoon) and we were allowed to take photos and explore the area in our free time.
Ayutthaya - Not bad if you are interested in old ruins (like I am) but it's not as spectacular as Angkor Wat. Definitely less tourists than Angkor Wat though.
Khao Yai National Park - this is a UNESCO World Heritage site, it's known for its waterfalls and population of wild elephants (I shot both). You can do group or private tours there. I did a private tour with a photographer (and his wife) which allowed me to spend as much time as I wanted in the various locations around the park. If you've seen "The Beach" with Leonardo DiCaprio the waterfall that they jump from is here. (However, there are many others).
Beaches - Based on the photos on your website, I think this is probably where you'd want to spend most of your time. I've been to a few low key ones (Ao Nang, Hua Hin) but I imagine you could go almost anywhere.
Cambodia
Well, even though I've been here three times, I've only ever been to Phnom Penh and Siem Reap (Angkor Wat), mostly because I was limited by the people I was travelling with, or I had very little time. I hope the next time I go there I can spend some time visiting other parts of the country.
Phnom Penh - the first time I went here (in 2001) it had a wonderfully faded colonial charm about it (in some areas). That's all gone now with all the construction and rebuilding. I suppose I might find something to enjoy about it if I had more time to spend there, maybe others can chime in. Of course, there are some interesting (and disturbing) places to see like the Tuol Sleng Genocide Museum and the Killing Fields.
Siem Reap/Angkor Wat - first time I went here (2001) it was a sleepy little town, very poor, and needy of tourist custom. I went there again in 2005 and 2012, and by that time the city had doubled in size and tripled in population. It has a much more slick tourism industry there, and most of the buildings you'll see (outside of the core) are all new buildings. Angkor Wat has of course, exploded with tourists, especially large groups of Chinese and Koreans, and no matter when you go, you will always be with hundreds, if not thousands, of other people. During Mar/Apr, there is no point in trying to get sunset or sunrise shots - the haze will prevent any interesting colour, and I have yet to see interesting cloud formations that would make it worthwhile. It would be much better to avoid those places (and thus the crowds) and head for other temples that will hopefully be less crowded. And I don't mean the other big temples like the Bayon or Ta Prohm - there will be as many people there at (or just after) sunrise as there will be at Angkor Wat (this was not true the first time I went there, but was definitely true the last time). I found it very difficult to get good shots at Ta Prohm - not only because of the crowds there (it's definitely the most popular), but because there are boardwalks and roped off areas that spoil the natural element of what that temple is about (definitely different from the first time I was there when we had to scramble over broken masonry to see a lot of the site). The movie "Tomb Raider" is good in that it shows a lot of the temples at the Angkor Wat complex at their best, especially Ta Prohm, but it definitely won't be like that when you go. In fact, in terms of crowds, I had a much better time photographing it in the late afternoon, rather than the morning. The other thing to be aware of is a lot of the temples are undergoing restoration work so there may be scaffolding up at quite a number of places. I did some homework before I went the last time, looking at places that other photographers have shot (like the ones John McDermott shot for his book
Elegy or any of Steve McCurry's work in the country) - this allowed me to discover lesser known temples that were much more agreeable to shoot. Of course, if you have a driver, it's worth asking him to take you to the kinds of places you want to shoot (which could include local villages, etc - I did that the first and second time there).
Vietnam
Well, I've only been here once, and that was 11 years ago now. Unfortunately I got a bad case of food poisoning here (in Hoi An) which severely impacted what I could do (and what I remember).
Hanoi - as mentioned above, this ended up being my favourite city in Vietnam. I love the mad chaos about it, the calm serenity around the lake (Hoan Kiem), interacting with the locals, and more. The experience felt not too distant to what it might have been like 20 or 30 years earlier.
Halong Bay - very disappointing. You will not get the iconic images you see of this bay at this time of year (again, haze). Grey skies, lots and lots of tourists, lots of boats. It's a real circus. This was the most disappointing place I visited in the country.
Hue - Had a fun time here, we did a motorcycle tour (hired drivers, we did not drive) around the countryside, through the rice fields. Definitely worth it.
Hoi An - Got sick here, but before I did, really enjoyed the town, the food, everything about it. Very laid back.
HCM City - Big, modern, bustling. Nothing impressed me here, although to be fair I only was here for 2 days.
Okay, this post has become very long, and I'm not sure I've helped you at all.

Let me know if you have any other questions.