First- what kind of rifle? If it is a Winchester 94 that is a bluing problem in its own class.
Re: Filling in pits before reblueing- it WOULD take welding. Done badly, changes heat teatment of steel. Done sorta OK, fill metal has a different alloy than gun, will show different color when blued.
I have done DIY cold blue, and it CAN do an "OK" sort of job. Metal prep, degreasing and warming without touching it with bare hands is critical. You will get a better job from a smith that does pro reblueing.
Now, if it is not a Winchester 71 or similar high $$$ rifle, you might consider an alternative finish, such as Cerakote. Or have a smith bead blast it, will hide the pits, and reblue with a matte finish instead of glossy.
What we have here is... failure- to communicate.