Trapper,
If you're having problems with your fish and their fins are shedding, do you mean they look like they're losing their fins? Are they tattered on the edges? Any number of things could be causing ragged fins: they could be nipping at each other (tiger barbs are notorious for this), it could be a bacterial infection, or it could be ammonia burn. I'm not sure if you understood the nitrogen cycle or not, but here's a VERY simplified explanation:
Fish release waste into the water and it's full of ammonia. Ammonia is bad for fish, as in toxic. There are a variety of different kinds of bacteria that convert the ammonia into nitrite which is highly toxic to fish as well. Different types of bacteria then convert the nitrite into nitrate, which isn't as toxic but still not good for the fish. You have to let your tank cycle or give the bacteria time to grow. The bacteria won't grow without a food souce, ammonia, so they won't start growing until you introduce fish to the aquarium. So what happens is you put in fish, ammonia spikes, bacteria start growing, the ammonia drops, the nitrite spikes, bacteria start growing, the nitrite drops, and the nitrate starts to go up. Bacteria don't spontaneously generate, and the bacteria that break down all the ammonia and nitrite don't float around in the water...they attach to solid surfaces. If you bring in some gravel or old filter media from an established aquarium, that will bring the bacteria in and speed up the process. You can also buy products like Cycle or Biospira to help introduce the bacteria as well. Your tank has to go through a nitrogen cycle.
I'd politely disagree with not using RO water for fish. I used RO water in my discus tanks for years, but DO NOT use straight RO water. RO water has no minerals in it, it's close to being pure. The fish NEED minerals in the water. If you do use RO water, there are products (something like RO Right) that you can buy and add then necessary minerals back to the water. If you do that, feel free to use RO or distilled water. If not, stay away from using it.
As far as the pH stuff, I wouldn't worry too much about it. Many of those additives people use for adjusting pH are not good. They lower the pH temporarily, and then it shoots back up. The constant up and down of pH is extremely stressful on the fish and can send them into shock and they could die. If the pH is a little high or a little low, that's okay for most fish (including tiger barbs). The best bet is to just leave it be and they'll be fine I would think.
If you're still worried about not meeting their specific water requirements, then maybe shift how you're looking at it. Rather than match your water to the fish, match the fish to your water. If Florida is sitting on a bed of limestone, your water as you can see has a high pH and is probably pretty hard. That's ideal water conditions for many Rift Lake African Cichlids, and then you wouldn't have to worry much about the water, but cichlids come with their own issues.