JB,
In this case, cosmetic reasons may be enough since this gun sounds very valuable.

Hopefully, the late RR wouldn't use "tempering" to describe hardening. It's my understanding that "tempering", as it pertains to steels, means to 'reduce hardness' to a desirable level.

Just my opinion, but each case of bulging should be assessed on its own to determine what level of detrimental damage has been done and what solution is appropriate. If this is a relatively small bulge, simply working it down may be all that's required.

After some recent and past posts on Briley's workmanship on things other than choke tubes, my choice of sources for this work would not include Briley.