Some cats may be able to get through the gastrointestinal (GI) effects of Tapazole, if they aren't too severe. My vet had us giving my mom's cat Pepcid AC to help with that. For some cats, the vomiting doesn't stop and the medication has to be stopped. It may be worth trying the transdermal medication. Since it doesn't go into the GI tract, it doesn't cause as much stomach upset. With my mom's cat (Hannah), she actually had high liver values along with the vomiting, and she wasn't able to tolerate the medication at all.
The site Pat & Alix mentioned also describes iopanoic acid as an alternative. You can get either medication from Island Pharmacy with a prescription: http://www.islandpharmacy.com/site/1...ge/769195/site
If your cat's kidney values seemed normal, I would discuss radioiodine therapy to see if it's an option for your cat. While it is expensive upfront, it can actually cure hyperthyroidism, so you won't need to give the twice per day medication for life. It shouldn't be used in cats with significant renal damage because it will reduce the blood flow through kidneys (hyperthyroidism increases the blood flow through the kidneys, so treating it should bring the blood pressure back to normal), and if the kidneys are significantly damaged, they may need the extra blood flow to function.
Since your vet is out of town, is there someone else that you can see--either someone in the same practice or someone else your vet recommended?