Ndking1126,
Cleanliness is next to Godliness here.
A couple of observations. That kind of muzzle leading is due entirely to the fact your crown is slightly recessed (by design to better protect it). The drawback is that in the short distance between the end of the rifling and the mouth of the tube, gas blow-by is erroding and splattering bullet base lead, so you will need to do this cleaning on a regular basis. Long ago I made a front sight extension for my Ruger Mk I target pistol. It always got lead caked up like that on the underside. All .22's make the splatter, but only the recessed crown makes it accumulate at the muzzle.
Don't even think about the drill trick unless you have some means of keeping the drill bit constrained to be coaxial with the bore, such as a lathe. If there is any off-axis wobble in the drilling you get a crown that isn't symmetrical about the axis. This lets gas start jetting past and cutting at the bullet base on one side just before it does so on the other. That uneven pressure tips the bullet as it exits, helping deteriorate accuracy. The uneven erosion of the base makes it wobble in flight slightly, making accuracy even worse. I have a home method of crowning described in a PDF file at my file repository. You can
download it here if you want to?
The old military barrels got absolutely terrible crown damage from sectioned steel cleaning rods being run into the muzzle by soldiers. I've seen some with no rifling left at all near the muzzle and the wear is usually uneven, causing the tipping problem. A drill run in deep enough will clean the worn area out. In a gun with a crown that bad, even a clumsy drilling job may be better than the worn crown, but one drilled true is significantly better. Either a special crowning tool with bore pilots or a lathe is still going to give the most consistently effective result.
For cleaning, see if you can borrow an Outer's Foul Out from someone so the barrel can really start with a clean slate? As an alternative, there is an actual lead solvent available now called
No-Lead. It is made by Sharp Shoot-R, under their Wipe-Out brand. You may need to plug the bore and fill it with the stuff and let it sit for an hour, but it should get the thing clean for you. When I bought some of this stuff, it came in two parts, since shaking around in transit apparently weakens it by releasing gas. I only mix what I will use in a session.
You don't need to clean the .22 RF every time, but it sure helps longevity to get a little oil in there. I don't care for the bore snakes personally, since I like to avoid brushing if I can. The Otis portable cleaning kits work with a self-loader though. The have a flexible pull-through cable with a pull-through jag and patches for it so you can clean from the breech end without worrying the crown.
Wear and tear is pretty minimal in a .22 RF anyway. I remember in Ed McGivern's book, Fast and Fancy Revolver Shooting, he showed before and after groups for a S&W K-22 that had something like 100,000 or 200,000 rounds through it that he'd finally sent to the factory for tightening up. Not much difference. Both good groups. Russ Carniak told me years ago that he expected a .45 ACP barrel's rifling to last at least 50,000 rounds shooting lubricated lead bullets at target velocities and pressures. It would need the lugs welded up and refitted from time to time, but the bore would be very hard to shoot out that way. I know those examples are handguns not expected to have the accuracy of a rifle, but I think you've got an awful long way to go with your rifle barrel just the same.
Can you post some after-cleaning pictures? The lead in the original makes the very ends of the lands hard to see clearly.