Or should I sign them as "for deposit to account# 12345 only" and send them to my bank in the states?

If you cash it here, you may have to wait 1-2 months.

That's after paying a fee that hovers somewhere around 250 baht.

May be less of a hassle to send them back home.

The last time I tried to deposit a US check into my Thai bank I got a very perplexed look from the lady who was taking care of me. I was invited to sit down while she had mini conferences with other bank employees. She came back with a bunch of papers and by that time I had been sitting for at least 15 minutes. She studied the papers and then started to go off for another conference. I called her back and asked her if it would be better for me to mail it to my US bank. That got a BIG smile and a nod from her. I now spend the 600 baht to mail the check via Thai EMS. It gets there in a couple of days and there is no paperwork or charges.