Another way, which will free up that contactor too, is to configure the Multi to ignore its AC input.
This is completely untested, but I’ve used this in the past to do something similar. What you do is you set up the General flag assistant to ignore AC-in 1.
Then you set up TWO relay assistants. One of them will drive the relay on, the other will drive it off. If none of the assistants match the conditions you set, the relay stays in its current state. Set these up to read the auxiliary input on the Multi.
And then you set the other one up the other way round, so you have something more or less like this:
Now remember the sense is inverted. When the “relay” is on, that means it ignores AC-in-1, so the grid is actually off. Conversely, when the “relay” is off, it sees AC-in-1, so the grid is actually on. Swap your configuration such that your Aux input works correctly with the GX device (I think it is the wrong way round in this picture).
Then simply connect the relay in the GX device to the aux input in the Multi. Now the generator start/stop function can open and close the contactor in the Multi itself.
Edit: The extra advantage of this, is the relay in the GX device sees only 5V. All the wiring is now low voltage.