Ditto on the RCBS press mount puller. It works so smooth and easy and does not mark the bullets. It's only drawback is that it wont pull lead boolits, but that's not your question.
I've always been of the mind that if you pull the bullet that you should resize the case (or neck) again. This may or may not be mainly a confidence thing. I like being meticulous with my hand loads, and especially Rifle cartridges.
You could pull the de-capping stem out of your sizer and do them one at a time pretty quickly, dump the powder in the pan and refill when you're ready to seat again. That's the other good thing about the RCBS Collet puller, your powder doesn't get dumped like in a hammer puller. It pulls the bullet nice and easy, and preserves the integrity of the powder charge in the case.