Ours broke 3 times soon after purchasing a brand new woodstove... The woodstove store handled it gracefully, and finally got the factory to send out a whole new woodstove door (determined that the door was likely warped/bent, and it was stressing the glass). No cost to us but time and frustration. But we saw that the replacements glass is over $200.
The glass is held with clips. You could create a metal insert the same size as the glass and clip it in securely... no need to weld. Then it could always be reversed if need be.
The one thing I'd mention is to make sure the fireproof gasketing is put in so that it creates an airtight seal. For a stove like ours (EPA-certified, non-catalytic), this is important to control air flow so the secondary "smoke burn" runs correctly.