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?
Push in 5e has much shorter distance, and therefore generally doesn't result in instant death. In scenarios like barge combat I wouldnt want to have to succeed in 3 saves per enemy or die.
I am all for making shove more like 5e, but as it is now
I feel that making it full action without further changes might actually make it worse.
When you simply edit the files to make shove an action rather than a bonus action : you cannot use shove twice with multi attack.
The game just doesn't allow it.
EDIT : But it's not as simple as I thought with extra attacks. You can attack twice but you can't attack once and shove once OR you can shove... but you loose your extra attack. Damn.
Is there a skill, spell or anything else you have in mind that is locked to "once per turn" ?
EDIT 2 : I have found a mod that limits jump to 1 per turn in combat. So I guess it could be doable for shove too... I'd have to try this.
