Cozen, be very cautious in moving anything from your old tank to your new tank. The life cycle of these parasites is such that the white spots you see on the fish are cysts which release "spores" that settle down onto the rocks / gravel / equipment where they mature and then release the microscopic critters that swim around and try to find a host (where they burrow into the skin and create new "white spots"). This is greatly simplifying the process, but speaks to the general cycle without getting into terminology like trophonts, etc. If you were to put the infected fish in a bare quarantine tank after giving them a full freshwater dip (3-5 min, depending upon the species), you'd likely see then next morning what appeared to be sugar on the bottom of the tank. These would be the cysts that dropped off the fish due to the freshwater bath.
It's really hard to get ood or crypt out of a tank once it is established at epidemic proportions, and some will say that the parasites are always present (much like cold germs are all around us, even if we don't have the symptoms of sneezing or runny noses). I've had good luck in the past by taking out all the fish and quarantining them in copper, with FW baths as needed if spots appear. If you do go the FW bath route, be sure to siphon the bottom of the quarantine tank daily to remove any cysts (and be sure to keep all your quarantine materials separate from the rest of your gear ... the cysts are sticky and you can easily reinfect your good system). Once all your fish are out of the tank, leave it completely free of fish (shrimp / crabs / inverts are OK) for 6-8 weeks. I actually left my tank fallow for 3 months just to be sure. If all looks good after the 6-8 week period and your fish have been clean for at least 3-4 weeks, you can re-introduce them into the tank and hopefully they'll be OK.
A couple other thoughts ... good to remove your equipment before medicating as the meds will soak into the plastic to some degree. Supposedly you'll be OK with the equipment if you give it a hot freshwater bath and then let it dry out. Garlic also works well in some cases as a preventative ... it is believed by some that the garlic permeates the skin of the fish (much like you might smell like garlic when sweating if you've recently eaten a meal with a lot of garlic), and this prevents the parasite from attaching to the fish when it is looking for a host.
Hope the above is helpful ... just one more perspective on what might help. These parasites are a pain, and only time and patience will help get your tank back on track.