Just show the home bank transactions, you should be able to print those. And match those up to the Credit Advice Receipt (which shows the source of the funds) issued by Bangkok Bank. And ask BBL to issue a Credit Advice summary letter, which details all 12 transfers.
Seems like a good question to ask Wells Fargo? How did you initiate this SWIFT wire transfer? Double-check the Thai Bank SWIFT code, account number and account holder's name. Twelve days for a SWIFT transfer seems unusual. IME it's ~ 18 hours.
Best to bring everything, including those things that "you've heard from people..." about. TM30, 90-Report receipt, lease, hand-drawn map, rent receipts, landlord;s Thai ID (signed), house book (signed), photos (of you in front of building). Each office may have unique requirements so you'd help yourself by sharing the office location.