A most unfortunate failure, but is all to common with bolts. Cause of bolt failures are usually over pressure or excessive headspace or metal fatigue. The method of failure is the right lug cracking, then breaking off, with crack starting on the back of the right hand lug in that tight radius where it meet the bolt body. I've never come across a USGI bolt that was either below or above hardness spec.
What maker's marks were on the bolt, ie who made it?
Did you get this carbine's headspaced checked before you shot it? You can still headspace it with the broken bolt, be sure to strip it first, and see if this was the problem.
Glad to hear you are getting gunsmith(s) to look at it, but make sure they know M1carbines.
If you have a micrometer, or vernier, check the outside width of the receiver in two locations, one right adjacent to that nicked spot, and the other more rearward, close to the web in front of the dovetail. What you are looking for is to check and see if the receiver has bulged out. If it has, your receiver is done. If it seems that it has not bulged out during failure of the bolt, you are probably going to be able to save this receiver.
Here's why: The recoil load on the bolt during the firing cycle is handled by the right hand lug, the smaller left hand lug is a guide for the bolt right after rotation, during recoil, so once rotated the left lug relief cut in the receiver aligns the bolt during its travel backward & forward.
If that nick is dressed out, the left lug of a replacement bolt will do the job. Do not have anyone attempt to repair weld that area, as it will degrade the strength in this region, put there by the original heat treating.
If and when you decide to get a replacement bolt, and you are not trying to retro-match it (ie flat Rock-Ola), get a USGI round bolt, and ensure that it's not a commercial one.