Zach...you may know this..but always insert your cleaning rods,brushes,jags,patches etc. from the bolt end. so everything travels the direction of the bullet. be carfull not to damage the crown of your barrel (it is the last thing a bullet sees as it exits the barrel, and damage can effect accuracy)
You should not require any tricks to push a wet patch through your barrel. Some patches are quite thick and others are thinner....I like the cotton flannel type. You should be using small .22 patches.
good luck, enjoy your pistol.. Aimhigh