If you don’t want a 12 gauge go to the 20 gauge.
The 16 gauge isn’t worth the trouble and most gun supply places don’t carry the 16 gauge.
I know someone will call me a liar about them not having 16 gauge ammunition, but where I live it’s 12 0r 20 ,16 gauge ammunition can hardly be found.
As a great lover of the 16 gauge I agree with you. The ammo is more difficult to find, and the selection limited.
If you plan to shoot it alot, you really need to roll your own.
Is the clay shooting going to be more for trap or for skeet? My experience is that with skeet, I go through way more shells and skeet action is lots faster than trap. A semi-auto is capable of the fast action of skeet so no hindrance on getting the shot in the air quickly enough. For a semiauto shotgun in whatever gauge you choose, I sure like my Browning (in 16 guage). I've also used borrowed Beneli over/under shotguns a number of times but my level of ability is not fine tuned enough to appreciate the difference between my Browning and the very fine Beneli.
Regarding the recoil, I don't perceive that much difference between my 12ga Winchester pump and 16ga Browning semi-auto. 20ga though has a noticeably lower kick and I wouldnt't be surprised if that is where you end up with on shotgun gauge.