I honestly I feel that with multi attack shove is better left of as bonus action. Being shoved 1-3 times per turn by one character would only make things worse. With how powerful it is I believe a balance would call for making it full action and not part of a multiattack - I do think that its power potential is on par with spells.
I'm not sure I agree - once you are shoved you have been moved away from the shover - so the shoving character would have to move to shove you again, possibly invoking AoO. I assume if this was an issue, then it would have been highlighted in 5E rules already? You also have to make an opposed roll for every shove attempt (it they implementy it as per 5E, not sure what they do tbh) - you may lose, and now you have sacrificed a melee attack. Of course, if you are standing near a precipice, it maybe worth trying this 1-3 times. But I could live with that - makes sense to me at least.
What I don't like is the low cost and the ballistic nature - I was def more than 5 ft away from the lava when my 2 charcaters were shoved into it.
