What proof is required to demonstrate an income of over 40,000 baht per month for a Non-O visa based on marriage in Thailand?

If you are using income earned within Thailand such as from teaching, Immigration will only consider your base salary and no additions such as a housing allowance. Also, if you are showing money earned from within Thailand, they will not look at income that you may be receiving from abroad. That's how it was at my Immigration office. Even though my total money received was well over 40K per month, Immigration would only consider my base salary from my school, and it was not enough.

solid proof of foreign origin

I'll go under the premise that you're talking about getting a 90 day Non-O visa INSIDE thailand:

IF you legally work inside the country (with a valid work permit) you show your contract, your pay stubs, the proof you've had thai S/S deductions etc.

OR

If you get the money from outside the country you either get the letter from your embassy stating you get an income of 40K baht a month and use that OR if you come from a country where your embassy no longer issues that notary letter (US, UK, Australia, etc) you transfer in to the country a minimum of 40K baht a month each month every month for the previous 12 months into a thai bank account in your name only.

SOMETIMES for the initial 90 day Non-O visa the immigration office will issue it with just 3 months of incoming transfers (because it's the first time you're applying for that visa)

Check with your immigration office well before you're thinking of applying for that visa