Yes, your 90 day report is approved. Now please print the next appointment page and carry it in your passport as you would carry the one if / when you did it in person.
I have an acquaintance who transferred money from UK to his KBank account here. Bangkok Bank was the clearing bank. He got his letter from Bangkok Bank and it was accepted at Chaengwattana. I know this as I was with him at bank and at Chaengwattana.
Two differences, though. He didn't use transferwiae. He used an agency in UK that gave him a good deal on rate and fees and the money didn't come from his account so he had to get a letter from them that it was his money and they were acting on his behalf.
And his was for an investment visa (bought a condo).
This was two years ago. Early 2016, if I am not mistaken.
I thought O-A was a multi entry visa stamping one in for one year everytime the holder arrived in Thailand: up-to the validity of visa. I'd suggest you to check if that is the case.
If you exit the country on your US passport without procuring a reentry permit (single/multiple), your extension of stay will be automatically invalidated.
You will have to take care of your 90 day report as usual until the time you're here on your US passport.