The lens mount of Q is 31mm and the focal flange distance is 9,2mm.
Lens mount - Wikipedia
So this leaves room for a bigger sensor. No idea how big or that even a 1" sensor could fit, but my guess is that it does.
Image sensor format - Wikipedia
I think a bigger sensor could give new life to the Q system. So the old lenses could be used on their limited size (7,6 x 5,4 mm or around 42 % of what a new lens could use). New lenses for the new bigger sensor.
Maybe turning the Q system in a nice cinema camera. But photography is also very important. I think 4k would be essential for a new second life to Q.
I think a 1 inch sensor (13,2 x 8,8 mm) could fit. That could be used to the full width for movie mode (12,8 x 7,2 mm -> 14,7mm diagonal, leaving room for sensor shake reduction) or for stills using a 4-3 form (11,8 x 8,8 mm -> 14,7mm diagonal).
With a nice set of lenses this could give Q a new life.