...you were talking through your buttocks!

Rule one on this board - engage brain before speaking.

Lunar escape velocity is 2.369 km/sec

If your trebuchet was 1 km in size, v^2=2as gives an acceleration of 2,750g
If only 100m in size, you need 27,500g. This is OK for solid objects but not for anything delicate

Escape velocity is monstrously large for any reasonable planet or moon. No nutty device with springs, elastic, bouyancy, or whatever will make a material difference to launch velocity requirements.

A device to achieve launch velocity needs to be physically big with large accelerations acting over long distances and times. To escape from the Earth, rockets burn for tens of minutes at multiple g's, covering distances of hundreds of km.

A mass driver, even for the moon, would need to be tens of km in size.

the main reason that Air-launch satellites work is that the mothership gets them above the bulk of the drag of the atmosphere, not that the escape velocity is appreciably less at a few km altitude.