you can't apply for the DTV while you are in Thailand. They will ask for proof of location (it doesn't have to be in the country that your passport was issued). We sent our receipt from our Airbnb, but they asked for boarding pass (Bangkok to Da Nang, Vietnam) and a picture of our arrival stamp. If you include all this when you apply, it will make it easier 😊
You get the criminal record clearance from your local sheriff department. Because this isn't common in the states, you may get a few weird looks and have to go to several different people and/or departments (I had to drive all over Houston to get mine).
As for the medical certificate, your PCP (primary care provider) or family doctor can easily do this.
You have to show your current location (Vietnam) In the next box they ask if this is your permanent address, to which you answer no and then enter your US address.
Having just completed this process, they may ask for 'further proof of current location' which included photos of passport stamp for Vietnam and boarding pass.
you can easily sign up for one of the soft power categories. On your first visit to Thailand sign up for a cooking class, or even Muay Thai (you can 'sign up and pay' but it's up to you if you actually attend) Then when you leave Thailand, you can apply via E-visa. There's a forum just for DTV on Facebook and there's a lot of examples of how to do it.
I'm a little surprised no one suggested the DTV since you mentioned you will be traveling. The DTV is a 5 year, multiple entry visa that allows 180 days per visit. And the financial requirements are much lower - 500,000 Thai baht in any bank vs 800,000 in a Thai bank. There are multiple categories to choose from to qualify. Might be worth looking into in your situation.