What are some using for this? I'm thinking a bench vise with grooved soft jaws to clamp the barrel is what I'm looking for? I currently use a lead sled but it's less than ideal IMO.
I have one of those Tipton gun cleaning cradle/vise things that just about everyone has one of and it works ok but it can sometimes scoot around on my bench and trying to hold it from moving with one hand and push a tight patch through with the other can sometimes be a PITA so here a few years ago I bought a set of V grooved soft jaws for my bench mounted vise and when I clamp a barrel in that it doesn't move.
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Ignore the description on the link, it'll take you to their VersaCradle gun vise.
This is the best Gun Vise I've ever seen or used. They do a poor job of marketing it, it's rare to see it in reviews or even mentioned. It holds the rifle in any position you want and actually holds it firmly. I use it to mount scopes as well, leveling the entire rifle is pretty quick and then the scope install is easy and fast.