I've only had dangerously bad headspace with one Mosin, a VERY battle worn M28-30 from the Winter War that appeared to have been fired until the barrel was melting. I fired that one with a string and it busted most every primer, making a mess but otherwise functioning OK. I've had a lot more headspace problems with rimless military rifles such as the Mausers. On Mosins you'll likely only notice it being more sticky.
To fix it you can simply use the go/no go to fit a new bolt head. This is what the Finns did. Of course you need a bunch of spare bolt heads to do it. This is one reason I stick with the SA label when possible. Or you can just use it if it's not too bad out of whack. I draw the line at burst primers or incipient case splits. Remember though you need to use BRASS cartridges to inspect for headspace related problems. Steel doesn't show you.
Is this a defective gauge?
Not defective, but possibly not really for a Soviet 54R. There are a number of rim style variations with that round if you notice. Some have a different shape than others. If your gauge is set for match level 53R, it may not function properly with a surplus Mosin. I don't use them for Mosins, though I always do for Mausers. For Mosins I rely on experience and do a check with a moderly handloaded brass round or three before firing in earnest. Visually check the brass in detail to see warning signs such as cratering primers (not always a problem) or the second line of stretch marks horizontal to the rim (big problem). I also check the brass for any weirdness that might indicate the chamber being out of round or chamber burrs.
Problem now is, I can't get the #%@$ extractor out. I let it soak on Kroil for a good long while. Still no bueno.
Use a vise and a brass punch. It just takes a few whacks in the right place and it will come right out.
Worst case scenario on this is a case separation and kaboom. That can end up injuring you, though I've never heard of any instance in any war or at any range of a Mosin bolt shearing its lugs, let alone shearing its handle/safety lug. The sheer size of that piece of steel makes sheering unlikely, so damage is going to be limited to your off hand and people standing near you. That said the untampered Mosins are incredibly strong. I remember a series of tests on the old collector's forum where a fellow intentionally plugged the barrels on a 91/30 and kept firing. It took multiple stuck bullets before it kaboomed, and then it just bulged the barrel. There are of course no guarantees, and good luck suing the makers ;-) But among the surplus rifles there are some I would NEVER put my face behind (the Krag for example) and some that don't worry me at all, such as the Mauser 98 and the Mosin 91.
