I received a call back. It seems that they both tested negative for both illnesses, and the Vet said that they looked healthy otherwise. He suspects they it may have been infectious bronchitis, which is why they sounded so bad.
I do however need to de worm my flock and also treat for coccidosis. I (stupidly) thought that cocci was only a problem in young poultry, but I guess if overgrown, it can become an issue. After describing my Turkeys symptoms to the vet, he suspects they may have Mg. He was also kind enough to say that he could help my vet prescribe something when they get the results in. Fingers crossed!