Here's a link that is pretty easy to understand relating to pre and post heating. If you decide to read it, mentally apply it to the welding of actions, as their thickness is an inch of more. It can help you get your mind around what is acceptable and what is not, as far as the reworking of actions. It's all about the stresses.
http://www.modernsteel.com/Uploads/Issues/February_2000/0002_04_funderburk.pdf

For the most part, I think action sides exceed their strength requirements by a great amount. Cleaning out pits, heating the piece to 212 or so degrees, and then filling the pits with a similar alloy will result in an almost indiscernable repair. Temperature gradients and contaminants are your enemy here.
It's been done since the change from muzzle to breech loading.

Out there doing it best I can.