Your wizz test is only good for so many days. When that comes a class date is going to be offered once the results are back.
I know you have an interesting situation. This industry really does like to keep you on your toes. I would HIGHLY recommend that if you take the contract job and the UPS calls that you do WHATEVER it takes to come to UPS.
There was a 3.5 week gap for me.
P.S. That recruiter can pound sand where the sun don't shine! They are only trying to protect themselves. Don't worry about X company telling UPS about you breaking your contract. It is against the law for them to do that and UPS act upon that knowledge.