I live in BKK in same situation as you and in my case the answer is: YES , you need the copy of Tabian Baan and ID of original landlord that should be signed by Landlord (+ copy of your wife id and rent agreement btw your wife and landlord).
This is not what I recommend to anybody but it is my solution to get rid of small headache 🙂
I usually let my wife (Thai) to check in hotel with her Id (No trace of me /my passport copy in registration of hotel) while traveling around. It has worked for me in few years , no problem until now.