What a coincidence! I just went through this procedure, I arrived from Philadelphia with my pet cat just last week. Regarding the USDA international health certificate you referred to this was the procedure I followed: had vet exam for cat with my local vet who then, using the VEHCS online system , electronically sent health certificate to the USDA Veternary (animal export?import) in Harrisburg PA. Regarding the 10 day validity period it is hard and fast rule, no change. What was done to elevate the time factor for US mail delivery the USDA Vet office required a FedEx overnight label which was sent along with the certificate request from my vet. This worked great as i had the signed certificate the next morning after it was transmitted from my vet to USDA Vet via VEHCS. There was no need for me to acquire the FedEx overnight label as this was included in initial application. Just be careful of holidays and weekends as the USDA vet is not available then. If Your vet is not certified on VEHCS it will cause problem with timing.
Everything worked out well in my case. The arrival into BKK airport the arrival process can be a bit frustrating though. The Thai animal import/export on their website says to pic up your pet at carrousel 8, what they mean is to go the import export office first with pet health certificate and Thai import permit and that guy will have you fill out another form and pay 510 thb then he will refer you to the oversized luggage office behind carrousel 15 were another guy will double check everything and then will go into the back and retrieve your pet. After getting the pet you to the red customs line where another official will go over all your docs again and give you another official form after you pay 1000 thb customs duty. Do not lose that form as you will need it if the pet is later exported and it will save you from paying another 1000 thb. So again although it was a bit bureaucratic bs it went well.
Hope this helps