I would come, visa exempt, then when you are here work out your future plans. I have a buddy that has a retirement visa. He tells me its better to get those in-country because of insurance reasons... That may not apply to you, now, but I am quite sure you can get a retirement visa while you are here. If you have a few extra dollars and don't want to be bothered, you can hire a visa agent to do it for you..
They've told me that a couple of times. I suspect if you came back in now, they wouldn't tell you that a second time. You should have a proper visa but they're pretty flexible.
The contract isn't necessary unless you intend to do all the immigration stuff yourself.
The contract doesn't have to be anything fancy and can be in English. Find a simple 1 page rental agreement on the interweb, alter it to suite your needs, print sign date, both you and your friend. You will also need to attach copies of the chanute and blue book, copies of the data page from your passports (both of your passports) signed. I may not have all the requirements right, it's been a couple of years. My experience with immigration is that they ALWAYS ask for more paperwork, so be prepared for that.
Years ago I looked into wife vs fiance visa. It seemed it was easier to get a fiance than wife visa. Someone once explained that the difference is with the wife visa they look at her background and with a fiance they look at your background. However, I have gotten neither and that was years ago.
From what I understand it's very difficult to get Thai girlfriends into the USA. So you should look forward to lengthy process that will likely end in disappointment. That being said, you do it yourself the first time, and if it works out you save $600... If it doesn't then you can spend $600 and see if that does it for you.
I get wanting to share the US with your girlfriend.. But when you consider expense and hassle, compared to other places, you may find going to other places is more appealing. Bali is Visa Free for your girlfriend and has much better beaches (as an example).
Sometimes different borders say different things. I once hired an agent to take me for a border bounce and on the return the told me which agents not to use.. So I am pretty sure different border agents do things differently.
I think they're refereed to as "Developing Country" or "Developing Economy". I think "third world" are more about peoples that are in a bad situation getting worse... Somalia for example (Or the US if you pay attention to US politics).