What are my options for extending my stay in Thailand after multiple tourist visa refusals and using all border crossings?

You could go to another country and apply for a SETV. Ho Chi Minh was pretty friendly.

Your name is Thai, I'm wondering if the visa refusal is somehow related? Are you ethnically Thai (or another ethnic group from Thailand) but have a UK passport? Is it a normal UK passport? I'm only asking this as I know Thailand has a lot of stateless people without citizenship and I wonder if this is related.

It's unusual you would have been rejected at Vientiane if you never got a visa from them before. They have tightened up on TR visas recently but rejecting you after one visa from the UK still sounds extreme.

If you do fly out and back DON'T fly into either Bangkok airport. I'd avoid Phuket too. Chiang Mai is probably safer. Few reports of the Isan airports but they are probably better than Bangkok. Fly into Bangkok with over six months here and you'll almost certainly be denied entry.

Ed visa is also a good option and should be no problem if you haven't had one before.

Fly out/in and get another visa exemption.

In theory, no limit. (Land is limited to twice per calendar year.) You may be questioned.

Where you at in Thailand? Phuket you can get an ed visa in the country and sign up for 1-3 months thai school

Marry her