The issue for the Immigration officer is to determine whether you're using repeated tourist visas or exemptions when your actual intention is long-term residence in Thailand without applying for a long-term visa. Some people get away with it as scrutiny is not always strict and thorough, but you've had a close shave. Decide for yourself whether a long-term residence visa is more suitable for your lifestyle choices, and get your act together on the financial requirements that go along with applying for it. Immigration have discretion to refuse entry if your pattern of travel indicates you're resident in Thailand without the correct visa.
If you're running out of pages, GET A NEW PASSPORT. Don't wait till the expiry date. Many countries will refuse entry if you don't have enough space for official stamps. A Lao visa for example takes up a whole passport page.
You can't apply for a visa for someone else. She has to apply through the visa service operating for the US Embassy in Bangkok. The key issue is that her application must prove she has strong reasons to return to Thailand. And you have a problem there because being your girlfriend means she has strong reasons to remain with you in the US. You must provide supporting evidence of your ties to life in Thsiland and hers, such a property, business, investment, family. The US Immigration are clued up about Thai girlfriends trying to get to the US so tread carefully and be thorough with the preparation and supporting documentation.
Why are you asking this question here, rather than asking the Thai embassy in your country? Or look up the regulations online. It's unhelpful to ask what happens next -- it's whatever you want to happen. Just don't be tempted to use tourist visas if your real aim is long-term residence in Thailand.
You've been with a Thai lady seven years. What do you expect will change by marrying her? How will you benefit? Is she rich? How will she benefit from being married to you? Think it through. It's not about birth certificates or identity. It's about property rights, money, taxation, inheritance......
What is the point of asking a question about marrying a Thai woman in Thailand and then add "excluding money"? The benefit for a Thai woman is all about money because it brings security and social status. No point asking the question if you exclude money from the answer.
You say you can manage the 800,000baht deposit, but you don't say if you have a bank account in Thailand. If not, you could have a problem finding a bank that will set up an account if you are on a tourist visa.
If you have the 800,000 on deposit you don't need the 65,000 income to get the visa. But do you have another source of income to live on? You can't work in Thailand on a Retirement visa.