Most consulates (however varies) wants the money in your personal account. Length of time seems to vary from 1 month to 2 months to 6 months, and will probably change again with new countries joining evisa
it is strange that it is taking them that long to supply an import permit. How long since resubmitting? Which airport are you applying through? I know the paperwork is site specific. I am American but been living in Cambodia, and have brought my two French bulldogs back and forth into Thailand multiple times - sometimes things have gone super smoothly and other times it feels like no one is on the other end of emails
You need an import permit from the Thai Government. Pretty sure the airport will be strict with that. Land borders are much easier (you are not bribing anyone at the airport). Other major issue is the airline. Will they even let you onto the plane without the import permit? Also, do you understand why the vet won’t do the health certificate? Are they correct in not doing it? If not, can you go to another vet? I also strongly suggest that if you plan to bring the pets back to the US at some point, that you look at those requirements now, as some need to be thought through in advance. Having certain paperwork before exiting the US makes it easier to return. Seen a few cases where families have had to abandon their pets because they didn’t think about the process of being the pet back into the country.