I'll say again - there is no perfect solution.
It all depends on which compromises you want to make.
To give you an idea of the limits of what can be acheived with a moderator, fire HV .22LR rounds through a moderated rifle: you still get a significant crack.
So perhaps the approach would be as follows:
1. You will never get rid of the supersonic crack of the bullet in flight. So decide on the maximim noise you're willing to tolerate from this.
2. From that, you should be able to work out which bullet size and velocity will give you that. There will probably be multiple answers.
3. Pick the cartridge and load that gives you the bullet size and velocity you've decided on.
4. Find the most effective possible moderator - ideally one that effectively gets rid of all of the detonation nosie, so you're still only dealing with the supersonic crack of the bullet in flight.
I'm going to hazard a guess that you will end up with a bimodal distribution of 'best' calibres: a handful of small calbres using small amounts of powder to chuck large for calibre bullets quite slowly (.222 with 60 grain, for instance), and a handful of large, really old calibres throwing heavy bullets at very low speeds (bottom end being something like .30-30 with 150gr).