By knowing you through your post and a gut feeling of your capabilities, fix the darn thing.I bought a product that has tiny diamond chips in it that you put in a wallowed out screw head to extract the screw. The product won't compress and actually temporary renews the slot by filling the voids.. I was sceptical when I bought it but it does work.
Yep, easy outs are a 4 letter word.Leave it alone or have someone with the equipment and skill to remove it do the job. Those spiral flute easy outs are a disaster waiting to happen.
You don't know what is underneath, and don't like what you see! No brainer to me, fix it. I would try to make a slot or drill some holes for tool grab to remove. If that fails, then drill it out. Just make sure you start with a small hole and work up your sizes so no damage occurs to the internal threads.
It's never a good idea to weld in or near a breech area in any barrel steel as you will alter the breech area metallurgical hoop stress strength.I'd take it to a really good tig welder and build it up and then file it flush and square using filing blocks and then blue it. You can remove the nipple to see the back side.
If you screw up the bolster trying to remove it you run the risk of ruining the barrel trying to replace the drum on a CVA.
That's what I would do. others will have their own opinions
If you do decide to remove the screw take it to a professional, you've already botched it once by using the wrong screwdriver.