Welcome to our Euro Venture!

When leaving the E.U. and going to Turkey, we of course had to obtain a health certificate for Sushi and Keno. While in Budapest, we read that the requirements are quite stringent. They need rabies vaccination (which we have), but also a rabbies FAVN (aka titre/titration) test, and multiple inoculations. The FAVN blood test is validation that the vaccination is present at a high enough level to prevent a rabies infection in the event they're exposed. Fair enough.

At the vet in Budapest, they were adamant that this test wasn't needed. We were skeptical, but also read many places online that customs doesn't check this at all, so we thought, "Why put the cats through a blood draw if they don't need it?". We were told that we'd need the rabies FAVN test to enter back into the EU. So, on we went, getting just the health certificate and booking the flight.
Enter flight day. And sure enough, no one cared about the rabies FAVN test. The airline inspected the health certificate and sent us on our way. Turkey's customs didn't look at anything. Home free!
Not so fast...
So, we arrive in Turkey and promptly contact a veterinarian to setup the rabies FAVN test so that we can get back into the E.U. in a few months. This is where the problems start...
In order to get a health certificate and Turkey animal passport, the cat must be registered. In order to register your cat, you need:
A Turkish credit card. THEY DO NOT ACCEPT INTERNATIONAL VISA/MC
A Turkish phone number
Get a foreigner tax ID

In order to get a Turkish credit card, you need a Turkish bank account. In order to get the bank account, you need to have a utility bill in your name, which we do not have!
Furthermore, there is supposedly a 90 day waiting period from the time the rabies FAVN test is performed to the time that you're able to enter the E.U...
Wait... what?
Let me get this straight. I have a 90 day tourist visa for Turkey, right? But I have to wait 90 days from the test date in order to get back to the E.U.? This implies that I need to register as a foreigner, get a Turkish national phone number, get a Turkish bank account, make a same-day veterinarian appointment all on our first day in Turkey!
This is logically impossible. It's mathematically impossible if you don't arrive in Turkey in the early A.M..
This is all very frustrating because it feels like it doesn't need to be this difficult. I can understand the need for us to register as a foreigner in order to make a tax payment, although we didn't need to do this in France or Hungary. Plus, registering as foreigner was relatively easy and able to be done online. But why can't you accept international Visa/MC and just charge a fee? And also, why must the phone number be Turkish? None of this makes any sense.
How could this have been avoided?
We should have done the rabies FAVN test in Budapest before we came. The test is good until the rabies vaccination expires (one year), and so we wouldn't have needed to do any of this.
What do we do now?
Well, we certainly have a problem on our hands, because we are near our 90 day limit in the Schengen zone, and will be over our 90 day limit on our Turkey visa by the time we're able to legally go to the E.U.. We can try to go to a non-EU country, like Cyprus, via ferry and hope that the border customs lets us through. We could also try traveling by car from Istanbul to Bulgaria in the hopes that vehicle crossing with the cats will be easier than by air. Our last option is to take a flight back to the U.S. which doesn't have the rabies FAVN requirement.