Hi Don,
If you are getting a 200gr bullet to go 3300fps in a 300RUM this must be a pretty hot load. (So, in general I would watch for pressure signs -this sounds like possibly the first.) But I'm not particularly familiar with that round.
It sounds like the cases are overexpanding and fusing to the chamber? Maybe others can chime in here, but you might try a more robust case. I'm not as familiar with the Remington cases. But I know that the Winchesters (at least the ones I've tried in my 300wsm) are on the soft side, and I would guess the Remingtons are similar. I've just ordered a batch of Norma cases. I know from the ones I've used in my 270wby that they tend to be harder and stand up to more punishment. They're more expensive, but a stuck case while hunting could really suck.
I'd also be tempted to take it to a good gunsmith and have him check and, if neeeded, polish the chamber. I've never had it happen to me, but I've heard reports of burrs left behind by chambers that have been reamed by a sloppy smith. The soft brass can fuse to those burrs and get stuck, making extraction sticky or worse.
Ben