There was an existing crosswedge in the tongue. Knocking the handle on and off, trimming, kerfing, and then driving the main wedge in didn’t knock it loose at all. I just left it as opposed to removing it and attempting to fix what wasn’t broken. After the first four times on and off the handle for fitting it was solid/tight enough to conservatively use without a wedge.
I was fortunate this morning and found a couple of hours of quiet to work a Cherry wedge into it.