Over cleaning or should I say over-zealous cleaning fucks-up more guns than a lifetime of actual shooting.
Do NOT remove a 10/22 barrel just so you can clean it from the breech
Keep it simple. A bore-snake, an OTIS cable kit, or a good one piece rod with a muzzle protector will all work just fine. You can also drill the rear of the receiver if you like. This was all good advice.
On my best, most precise 10/22, I thoroughly clean about every 400 rounds or about every third or fourth trip to the range. For me this keeps my action running smoothly and my groups consistent. Otherwise, it gets a simple wipe down and a drop of oil before going back into the safe.
On my plinker 10/22, I clean when it starts to run sluggish (maybe every 1000-1500 rounds). I will add a drop of oil every now and then if I think it needs it.
As always- YMMV