Hey,
I was very surprised to find this item in my last playtrough. I think it was somewhere in Grymforge.
Won't talk too much about shove again but seriously, you are over doing it...
Being rewarded when you shove does not make any sense lore-wise and it also offers a painfull gameplay. Shoving each turn to have +1 AC ?
I think you should turn it into a Ring of Protection that always gives +1 AC but also +1 to ST.
Players need to feel that they become stronger. A better AC makes our character stronger but a better AC only if you shove is often useless.
As a regular Ring of Protection it would be a very good reward for level 5 characters exploring a dangerous dungeon without the chore of having to shove at each turn to be more powerfull...