.22 Mag should need to be cleaned MUCH LESS than the .17HMR!
If it was a .22LR, almost never.
For cleaning, try getting a bore snake, but cut off the metal-entangled end and just use rough cords to 'swab' your .22 bore
always cleaning from the BREECH whenever possible! Except for an occassional patch dipped in solvent, the bore snake is all you should need
90+ percent of the time to swab a .22 rimfire bore.
As for the .17, personally I've never shot one but the advice already given agrees with what I frequently hear about their care and cleaning and accuracy.
Are you keeping notes on your findings too?
What ammo is cleaner than others?
More accurate?
Any changes in quality? whenever you buy and shoot new lots of ammo?
Etc., etc.