Can I change banks during a visa extension renewal in Thailand without issues?

There's no issue switching banks BUT I would move the money in 400K baht increments

I say that because the seasoning terms for banked money method are 800K baht in a thai bank account in your name only for 2 months before you apply for the extension, then you keep the 800K baht in the account for 3 months after the extension is granted and after that the balance can't go below 400K the rest of the year.. <- That's the reason I said move it in 400K increments.

That way you ALWAYS have the 400K required funds banked (in one bank or another). You could take out 400K go put it in the new account, then a few days later do it with the remaining 400K.

IF you switch bank accounts you will need DOUBLE the bank document requirements because you have to show the funds in the old account and the new account so you'd need two bank letters, two yearly detail transaction reports and to update the bank book of both accounts the day you applied for the extension.