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.
