Being that the barrel is threaded, and guessing for a can, does your can spin on and take up about the same amount of room in the end of the forearm as the thread protector.
I ask, since normally you want the threaded section of the barrel to end just in front of the forearm so you don't end up with any contact to the forearm from the can.
Also, so you don't get a major shift in POI between running a can and not, do a single imbed tension point to the barrel just before the threaded section when you go to bed the action into the stock.
Hence Do the action imbed first with a credit card thickness shim just before the threaded part of the barrel so the barrel will free float in the stock forearm. Once that has set up, mill a 1" long and about 1/2" wide channel for the bedding tension point, then use about three shims worth of cards to pull the barrel sightly up as you do the tension inbed, which will have the tension point to the barrel from the forearm with about 1 credit card worth of shim in the end. Your still going to have a slight shift in POI, but it will not be as major as the barrel free floating and then adding the can weight to the barrel still free floating next instead.
Hell, truth be told, with the stock forearm as thin as it is, would just channel down the entire forearm to bed in a steel rod first*, which will really stiffen the forearm to start with. Then with the forearm stiffen first, would add in the single point bedding afterwards.
* You already added the cap, but on the next go around, you can drill the channel in the forearm, glass in a steel rod, then the cap will hide the rod/glass/channel instead.