I don't understand really the question in that case where a Prince is promotted to a Prince, meaning it actually refuses the promotion. In this case, it doesn't mind if this (non)promotion is obtained when entering, staying or leaving the zone as the piece is unchanged. What matters is that the piece should not be immobile!
Now look this unfinished page (the GC is not set yet). For the ID, I have used the morph instruction instead, and in this case it seems to work, the Prince can be promotted to either a Queen or remain a Prince, and it can move afterwards.
I don't understand really the question in that case where a Prince is promotted to a Prince, meaning it actually refuses the promotion. In this case, it doesn't mind if this (non)promotion is obtained when entering, staying or leaving the zone as the piece is unchanged. What matters is that the piece should not be immobile!
Now look this unfinished page (the GC is not set yet). For the ID, I have used the morph instruction instead, and in this case it seems to work, the Prince can be promotted to either a Queen or remain a Prince, and it can move afterwards.
https://www.chessvariants.com/play/timurid-samarkand