I came to the similar idea (as like as enjoy the concept). As advice, I think you should change player’s position based on object scale. I mean, if a player stands on the edge of a block, when it scales, the player needs to stay on the edge. To achieve this, I ray-casted block under the Player and change the position based on Transform’s basis (Godot terminology). In code:

var origin_offset := global_position - ground_transform_previous.origin
var basis_change := ground_transform_current.basis * ground_transform_previous.basis.inverse()

var player_offset := basis_change * origin_offset - origin_offset
global_position += player_offset

Also, for scaling I use mouse wheel.

This game has a great deal of promise, but it needs some time to really flesh out the platforming. Right now it is too rough for me to really enjoy.

It would also be really improved with some sound, just a simple loop music playing and maybe a boing for jumping is all it would take.