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Might not be the stem itself, but an injury near the stem, and you hear the air escaping through the stem-hole in the rim... ( had this happen on several tube-tires on different vehicles. ).
Since you will likely have to break this wheel down again, when you get the tube out, check it over... if indeed the stem is damaged, you only option is probably to install a metal stem.
As for the base of the stem being wide and tending to get in between the tire and rim, I have a "stem puller" handle used for popping tubeless stems into rims, which I screw onto the tube stem(after threading the stem through the rim), and use that to push the stem deep into the tube while working the tire onto the rim...
Hope you can get it resolved !