Just working off your diagram and did not look at your pics.
While it may look confusing at first, it’s a bit easier to understand if you disregard the constant hot feed for the unswitched half of the receptacle. I took it out of your diagram so it’s easier to see:
So your hot starts in the left box and gets switched over the two travelers to the right box and goes out the common terminal to the receptacle. The only thing that’s different from what you usually see is that the neutral doesn’t start in the left box.
So while I think it’s possible you can do this with a dumb switch, I can’t quite visualize it at this point. It would take a lot of rewiring at the switches.
The easier solution might be to do this with an Aux instead of a dumb switch, as you only need two conductors between the two switches. I’m not sure if/how an Aux does with a switched receptacle. Perhaps @harjms can comment here.
So what I’m thinking is that using an Aux you have a Line/Load in the same box (which in your case is the right switch box):
Speaking theoretically, the Inovelli would go in the right switch box. You have a hot and a neutral there. Leave the neutral to the receptacle as is, pigtailing for the switch. The black presently going to the switched receptacle gets connected to the Load on the Inovelli.
Now you just need to send a neutral and a traveler to the Aux. Use 2 of the 3 conductors on the 3-wire between the switches.
Make sure you have lots of pics and labels if/before you start taking this apart.