Ironically, in that fight if you moved Shove to 5E RAW they'd actually get to shove twice as much because of Extra Attack. Realistically the only way to fix that would be to reduce the launch distance of the shove itself.
But that's the point. Or at very least one of the main points of contention.
Shove should just allow to push someone 5ft/1,5m away, not to YEET the poor bastard into the stratosphere.
And "being careful of the edges" should simply mean that you shouldn't linger less than 5-10 feet next to one, not that "Anywhere in a five meters radius is potential insta-death".
To add insult to the injury, the wonky physics implementation in the game make it so that things don't just fall (mostly) *vertically* as they should, but gain significant horizontal momentum when height is added to the equation.
Which in layman terms means that an already ridiculous 4m/20ft shove can turn into a 20+ meters throw if some height is involved, turning whoever is doing the pushing in an human trebuchet.