The "cleanest" powder I've ever found that you can shoot from a caplock is American Pioneer Powder. This stuff almost makes the barrel "slipperier" rather than fowling it. I don't know what is in or not in it, but the HUGE drawback is that w/90 grs behind a .54 roundball I chrono'd it at only 1000 fps, give or take. The same load with 777 is 2000 fps give or take. I'm just not willing to give up 1000 fps for any amount of cleanliness! I also found that ignition in small bores, like my .32 or .36 was inconsistent with Pioneer.
While others here have the experience that 777 is "cleaner" than real bp, I haven't found that in my shooting. However, 777 does not have that strong sulphur smell, which sure makes my wife happier when I clean guns in the house. Overall, for a caplock, I don't think 777 can be beat and you can buy it all over, even at big-box mart.
I do use Goex in my flintlock as Hodgen doesn't even recommend 777 in a flintlock unless you pour a little real bp in first, and who's going to mess around with that.