No surprise it jumped. They are good jumpers and the new home would be deemed way too small by them.
As for parasites, it is indeed a risk, always a risk even after treatment and qt. No medication will kill all of pathogens and no med will kill entirely any one particular microscopic pathogen. With macroscopic it is quite possible though.
Metro + prazi would be best to be administered internally, with food. A long-term bath would be about 100th - 1000th of an efficiency of an internal administration. For external I'd use potassium permanganate, three 15 min baths 2 days apart. Let me know of you want to know the concentration. Carp can handle that no problem.
Flubendazole is banned, IIRC (maybe not) but Fenbendazole is a safer and more efficient alternative.
Bifuran (may be banned too) for gram-positive bacteria. Erythro for gram negative (oxytetracycline is the older generation alternative but erythro appears much better).
If the carp will go into an outside pond, which is already teeming with parasites, I'd scale down these efforts by 10x.