There was a thread a few months back about using 1NT as Gazilli after a 1♥ opening. In combination with 1♠ as a F1NT response, that gives a complete framework that works for both 1M openings within a 2/1 framework. In the previous thread, I also discussed some optimisations here, such as using diamonds as the anchor suit (instead of clubs) and reversing diamonds and spades in the follow-ups. These amendments are designed to minimise the differences between the structures.
To be honest though, I am not sure what Gazilli has to do with the methods being suggested here. The convention solves particular problems on Opener's rebid; their idea simply creates new problems.