777 primers were designed to be used with 777 powder. They seem to reduce the 'crud ring' some. They are not intended to be used with BH209, and shouldn't be.

You can clean your breech plug any way you wish. Just be aware that the flash hole will carbon with 'hard' carbon that almost seems like it is the breech plug it is so hard. The flash hole will close down to a much smaller size because of this. Be aware that a hole with a 1/16" diameter has just 1/4 the area of a 1/8" diameter hole which is what the breech plug starts out with. Most spin their 1/8" drill manually so as to avoid the 'scratching' you are concerned with. Myself, sometimes, i spin my drill with a cordless drill motor cuz it is easier. Does it cause the hole to carbon quicker? Perhaps. I don't really know or care. My Omega is 100% reliable for more than 20 shots during trips to the range or during hunting season, and when the fire hole gets too plugged with carbon, it tells me, by spewing excessive blow back.

Whilst shooting BH209, the breech plug fouling is really the only issue one needs to concern one's self with. Barrel fouling is a non-issue; myself, i have never reached a point where i couldn't load my Omega, because the barrel was too fouled. Loading doesn't get any more difficult after some 30 or 40 shots; it is conceivable one could go a hundreds or more shots without cleaning the barrel. Just don't clean your barrel with traditional black powder solvents! There have been instances where folk have experienced rusting after using BH209. It is my opinion that it was mostly caused by using the wrong solvents, and/or lubricants. It seems the jury is still out on this issue.