Brokennock
Cannon
If I recall correctly, you're hunting over a pretty solid pointing pup. The cows knee suggestion seems like a good one. Combine it with something better to seal the threads on the "pegs" and you should be able to pull the knee off when the dog gets birdy or goes on point enabling you to make the shot at the flush.The anti-seize is a cream consistency, non-petroleum with suspended metal particles. I've used it for years and never had an issue with it in dry weather. The musket caps are no slit or slotted, it is a solid top-hat that should have helped keep water out of the actual peg. The only place water is likely is where the pegs thread into the breach. I thought the anti-seize might help to an extent but alas it did not. I do not upland hunt in rain often, but this was a trip a long way from home and it was 70-degrees and hardly any wind - not the freezing rain scenario someone mentioned. I have real pure bear grease. I also have waxes. Both sound logical. Next time I will put a dab of bear grease around the base of the peg and over the whole capped peg as well. I'll also experiment with putting wax around the base of the peg either on my second gun or on another rainy day. There are times when I have too much invested to sit in the truck or camper and am willing to take a chance in the field, wet or not.
Another option, that might be good for the your person as well, would be a rain poncho,,, wear it over your bag and horn and keep the gun under it until the dog show interest or points.