I'm guessing it's ok, but I figured I'd better ask to ease my mind.

So, when I chamber a round with the safety on, it's a lot harder to do than when the safety is off. Is it ok to do this, or am I stressing some parts, and potentially doing damage?

The bolt will cycle with the selector on SAFE or FIRE. The selector holds the trigger bar down (trigger forward) so it can't move. The bolt pushes the hammer down past the cocked point to the disconnect point. That's the little click you feel as you release the trigger following a shot. It does take a little more pressure to push the bolt down that last fraction of an inch.

Barring some anomaly in your rifle you can't hurt anything.

If you can put the selector on SAFE with the rifle not cocked there are problems.

-- Chuck