Before I got full length tubes, I shot with short inserts (Savage Four-Tenners). As I recall, there was little difference from the expansion chamber effect.
At the shotgun forum, short 12-ga inserts, in rifle and pistol calibers, are discussed from time to time. As I recall, nobody commented on the sound signature being significantly different when shooting the shorties in 12-ga barrels.
The aforementioned H&R 10-ga comes with a screw-in choke. You might fab a wiper assembly to replace the choke. It could work in most 12-ga guns, too.