Grinding is the only way. Even if you welded over the area you still have to grind it. Be sure to feather it out so it doesn't look like a deep pock mark.
I wouldn't even worry about it, it's only going to be visible to you and your fellow reenactor? I'd be happy I had a 1919 at all.
If you go this route I might try JB weld instead, but if you're goin to all that trouble you could always get a repro left plate.
I'd probably just weld them up and refinish, the darker the repark the less likely you are to see the heat marks anyway.
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