Try using a poncho when you are in the rain. You can keep the rifle under the poncho to protect the action, while the barrel sticks out but is held down while the water that does hit the barrel runs down to the muzzle and drips off it. As long as the muzzle is down you are not going to get anything more than condensation in the barrel.
I recommend usuing a cleaning patch with lots of lube on it to lubricate the bore of your gun after seating the PRB. That protects the bore from rusting in a humid environment. Then use tape, or condoms-- if they worked for the GIs in WWII, they will work for you--to seal the muzzle of the gun. To keep your powder dry, you might want to have a cap to go over the percussion cap to seal the nipple from mositure. Those triangular pencil erasers made of rubber will do the job, but you may have to cut down the top for your particular gun. There are several kinds of cap Kappers sold, so check the suppliers. And the Cow's Knee, a piece of leather that is shaped like a hat, with straps hanging down to tie under you gun can be put over the hammer and nipple to keep it dry. The leather is usually coated or soaked in oils, and wax to waterproof it.
I think a small- postage stamp sized- piece of plastic wrap can be placed under the cap and on top of the nipple to waterproof the flashchannel. The fire from the primer will burn right through the wrap, and ignite the powder in the barrel. The rest of the plastic wrap will burn partly and fall away from the nipple. Certainly on a rainy day you don't worry about starting a fire with it.
Or, you could put plastic wrap OVER the nipple and hold it in place with a rubber O-ring, pushed down over the nipple. That would eliminate any concern about the plastic wrap cushioning the cap enough to cause a misfire.