Pond, try to get your hands on a smaller patch jag, and some smaller patches. Stick with brass, if at all possible. The plastic tools never last long.
And, don't worry about the rod touching the lands in the bore during normal cleaning. It won't hurt anything, unless the contact is being made by a sharp edge.
As Art said - it's the crown and the chamber face that are damaged by poor cleaning methods.
For fussy .22s, I use a plastic muzzle protector/bore guide on a 17 caliber t-handle cleaning rod.
For most .22s... I just use a .22 caliber Gunslick stainless steel cleaning rod
. It rides .22 bores very nicely, and I don't need to use its brass muzzle protector/bore guide.
If a patch is too large, it simply will not fit in the bore. It's not a matter of being incredibly tight; it just will not
fit, if it's too large.
In my opinion....
Using a boresnake for regular "cleaning" is about as effective as "changing the oil" in your vehicle by doing nothing more than replacing the filter and running the oil through some cheese cloth. You feel like you accomplished something but all the crap that matters is still in your bore/engine.
I've been using boresnakes since '98 or '99. I have never found them to be a suitable substitute for proper cleaning tools.
One in good conditions is great for getting powder residue out at the range, or to remove bore debris while hunting; but they don't clean as well as traditional methods.
Plus... cleaning chemicals and crud from the firearms' bores will
cause deterioration of the boresnake, over time. Eventually you'll find yourself following the lead of other 'dedicated' boresnake users, trying to figure out how to get a broken snake out of the bore.
Worst of all... 22 caliber bore snakes seem to be the most prone to breakage, and
the hardest to remove.