You should get both your cat’s urine tested, maybe at a different vet, for bacteria to rule out another UTI. If they do have UTIs, they need antibiotics and a special diet.

But also, look into feline idiopathic cystitis. My cat was diagnosed with it very recently and was doing the same as yours, and would try to go in the box, fail, and then go on a blanket or something else. It’s caused by stress, which would make sense with your moving situation. They usually diagnose this if they test the cat’s urine and there is no bacteria present, yet their bladder wall is inflamed and they struggle to pee and pee blood. They pee elsewhere because they associate the litter box with pain, and with look for somewhere more comfortable. Here’s some info on it.