Using instance variables with live_execute_string has been broken since 2.3. I don't know if the problem is with GMRoomPack or GMLive, and I don't think Yal has fixed it yet.
I managed to get it working with another one of the recommended solutions found in the documentation, but that has since stopped working again. Though I think the problem in on my end since I haven't updated either of the extensions.
This was the one I tried with: https://github.com/GameMakerDiscord/execute_string
See if you can get it working for you :]
Correction: It never really stopped working. I just found that I had commented some code for testing, then forgot about it. Another note though, my current solution only works with YYC, not VM.