@Fractal, I know this is almost two years ago, and it looks like you didn't find any solution to OSD issue.
I didn't use my 2221A for a while, but last week when I needed it, I had same issue with OSD disappearing, maybe little bit different issue than yours, on my 2221A the whole screen goes blank after +/- 8 minutes usage, when I turn it off and on again, the analog part starts working but not the storage part anymore, I had to wait till it was cooled down to get OSD working.
That's why I ended up in your topic here, and I think I found a solution (at least on my 2221A)
After checking the service manual, the OSD is running through a Display Controller chip (U9208), the only chip with a heat sink on the storage board (if you can call that a heat sink ofc).
I took a temperature measurement with open case, in my fairly cold hobby room (16 °C), after 30 minutes the temperature on the heat sink raised up to 42 °C and stayed around that after 2 hours testing, the OSD didn't crashed with open case, the chip should handle that easily, but the measurement was on the heat sink and not directly on the chip itself and the case was removed, I think after a while things get old and the chip can't handle the heat anymore, or maybe the thermal paste between the chip and the heat sink dries out. I couldn't find a way to remove the heat sink without damaging the board, so I didn't touch that.
I thought, why not put another heat sink on top of the existing heat sink and see what happens, I didn't have any matching heat sink, the original one is 30mm round, but I had some Rasberry Pi 4 heat sink sets and some of them are 15x15mm square, I put 4 of those on the existing heat sink and put the case on.
I did a 3-hour test run in storage mode to make sure that the display controller got used and OSD didn't crash anymore, it looks like the issue was the chip getting too hot, I am not sure if it helps with your 2221A, but you can try.
Just be careful when you use a heat sink, make sure it is not higher than 4mm otherwise it will hit the case, and also make sure you have a good heat sink with strong thermal double-sided adhesive tape on it.
Disclaimer: I won't take any responsibility if something goes wrong, it is up to you if you want to try or not
Here after 2 hours testing:
Heat sinks on top of the original heat sink:
After 3 hours testing with case on 2221A, still working without issues:
A side note: I did remove the pouch from the case, it looked cleaner to me on the bench without the pouch, I am not sure if removing the pouch also helped with heat escaping.