Doc I also have a 300Wby (grand ol dame of "Super 30s" if you ask me) and I likewise used the "5 minute rule" with it as well. I dont suppose its technically a 5 minute rule its more like this.

When I shoot/sight in I typically carry more than one rifle. Not only do I shoot more with multiple guns, I get equal practice but fire fewer rounds (generating less wear and heat) from each gun. 20 shots worth of practice is 20 shots, be them all from one gun or 10 in one and 10 in another etc... I keep my guns "field clean" with a boresnake for each gun. I NEVER run any type of cleaning rod, snake or solvents through a warm/hot barrel. I typically setup at whatever yardage and then fire a shot. (Two is ok but I prefer only 1 as it simply cant hurt to keep a barrel cool can it?) I then pick another target (I like to use the sight in targets with the smaller targets in each corner of the main target) and fire another gun at it. That way I can remove the bolt from each gun and set it aside (if any wind is present I aim it into it and if its really hot I put the black steel in shade) and fire another gun. I then go down range and cover the holes with masking tape and repeat the process. So sometimes I might fire one gun every 5 minutes or it might be as long as 10-15 minutes between rounds.

The faster the round the more heat it generates but I use the same protocol for ALL my big game calibers. Clean, cool barrels just last longer!
RA