I make all my rods tapered with a brass fitting on the small (inside) end. I use the small end to push the ball down, so I don't have to flip the rod to load, and then again to return it to the stock. I am unconcerned about any fouling that goes into the rod hole.
The new cloth will have sizing in it, and will be stiff and feel thick. Washing the material in cold water, and hang to dry, before cutting the patches removes the sizing, and any shrinkage is minimal. If you use hot water and a dryer, yes, you'll shrink the material, and likely increase its thickness. So, cold water, and hang to dry.
The fouling from black powder sucks moisture out of the air - that's what you're seeing in the pan. None of the liquid from your patch exits the vent.
90-95 grains of FFFg is a pretty stiff load for punching paper, though it will be close to your most accurate load. My .50 cal Virginy likes 85 gr. FFg GOEX, so you are in the right neighbourhood. But try FFg rather than FFFg.