Can I apply for a new NON-O visa in Bangkok while on a NON IMM Re-entry permit?

You're not on any Non-Imm visa :( IF you have a re-entry permit I believe you are actually on an "extension of stay" (LOOK in your passport). You will not be applying for ANY Non-O VISA at all just a new yearly extension.

You can apply for a new yearly extension of stay when you have 45 days or less left on your current stamp. So in your case with an extension expiring on July 21 the soonest you could apply would be Monday June 7th. (You do NOT lose any time applying early, they add the extension to your current expiration date

You need the 400K baht in a thai bank account in your name only for 2 months before you apply. You apply for the year extension, you pay 1900baht and you will get a 30 day under consideration stamp. When that stamp runs down you go back (with an updated copy of your bank book showing that the 400K baht is still in the account) and they will ink the year extension into your passport

Take your thai wife and go to Chaengwattana to get the hand out listing the requirements for the documents and bank letter and photos, etc and have your wife ask if anything is needed that's not on the list.

You have plenty of time before you can apply to get out there get the hand out and work on getting the documents together.