I too shoot one of the Investarms .50 Hawkins and have found 60 grains (and remember this is by volume) of either goex or 777 under a .495 rb and .018 patch will shoot a ragged one hole group @ 50 yards, if i do my part. It doesnt like pyrodex as well though and groups open up a little.
Loading down to 50 grains of goex shoots about as well though poi at 50 drops about 1 1/2 inches. 70 grains of either the goex or 777 hit the target at the same poi though groups open up a little and are good enough the 70 gr. load will be my hunting load with either powder.
With the Goex i have to moist/dry patch every 3 or 4 shots to keep fouling and difficult loading bearable but that seems to be the nature of "real" black powder.
Ive had the best luck with remington caps, cci's tend to have some misfires, and trying the cci magnums didnt help in that respect. groups opened up with all powders using the cci magnums also.
For cleaning at home, I use hot tap water, with a bit of dish soap. initially filling the bore with soap/water and letting it stand for 10 or 15 minutes. my procedure is to use a piece of clear plastic tube over the nipple into a jar of hot water soap mix, and i prefer a rigid aluminum shotgun rod with a bore guide and a 28 guage bore swab as it fits the barrel tightly. i'll use the bronze brush initially to loosen any remaining fouling, then swab the barrel using the above mentioned rod, with the tube in a jar or milk jug, i then get a siphoning action when pumping the rod in the bore, and you can see the fouling collecting in the catch container.
After scrubbing with the soap mix, i swap to plain hot tap water, just pinching the tube off with a clothes pin, again fill the bore and let it sit about 10 minutes, then repeat the scrubbing process. and continue to do this until the water in my catch container remains clean.
the last thing i do is repeat the swabbing with rubbing alcohol, to help remove any remaining moisture, several dry patches down the barrel, and in an hour or so lube patch to prevent rust.
Next then is remove the nipple and soak it in alcohol, wipe the exterior of the rifle as needed with alcohol soaked rag, to remove exterior fouling, and lightly oil wipe all exterior parts. then clean and dry the nipple and reinstall.
Note too, for a cheap effective bore guide, cheap plastic funnel, cut the spout, to just fit inside the bore, and cut down the mouth of the funnel so its an inch or so tall.