I don't ever take barrels off.
I've been using the magnetic flusher sold by a member in here, davec2, and it works really well:
LINK TO FLUSHER
Here's the way I clean my rifles - just my 2c, YMMV:
1. I pull the lock and clean it with straight Ballistol
2. Place the magnet over the hole, blow thru it to make sure youre over the vent.
3. Place the tube clunk in hot water w/Dawn
4. Orient gun muzzle low w/vent down. Pump back and forth w/patches until clean. Make sure dont knock magnet off-center.
5. Real good generous water flush shot of WD40 after.
6. Dry patch and QUICKLY, to avoid flash rust, swab with RIG patch with a shot of WD40 to saturate and dilute a little.
7. Re-assemble, wipe all over gun w/Ballistol rag, give 'er a good rub down with an old t-shirt, store gun muzzle down for a day or 2.