That's a heck of a nice-looking tool,great job....
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.