The other night I went through my tool box and found a proper size allen key. I stuck the short end in a vise and bent/twisted it until the long end points straight down when the latch is closed, it needed about 30 degrees of counter clockwise rotation. I'm currently leaving that key in the latch all the time. The outer door does hit it and is about 1/4" short of closing completely, but it's not noticeable at all unless you look at the magnet catch on top.
So far it hasn't gotten very warm at all at the end while the stove is running, but the weather is still moderate and the stove isn't going full blast yet. Will have to see how it goes as demand goes up.
The bending process was iffy, was expecting it to break at any moment, and the vice jaws chewed up the end of the key which required filing to get back to something that would fit. The fact that the flats are now twisted limits how far the key will enter the socket on the latch as well. I suppose one could shop around and maybe find a manufacturer whose keys happen to be bent on the proper angle already, or maybe apply some heat and custom bend a straight piece of hex key. If this proof of concept version is workable, I may spend some more effort on improving it.
Interesting, I've thought of doing something similar.