Thanks for taking the time to play!
I think it feels particularly difficult on Emulator.js on keyboard. Something seems slightly off making the wall grab much harder there.
Feedback elsewhere about the wall grab on shoulder was similar. I think fluidity would be improved by allowing hold DPAD in the wall direction to do a wall slide, and then L is reserved for a wall-grab, to hold in place. That ties in with the desire to have a projectile power-up that you can aim when wall-grabbing (so hold L to stay in place, and use D-PAD to aim)
A cut feature was to be able to pull items as well as push them, and L is intended for that too. I got the physics working (which if you go left from Player start you can see, if you haven't tried that!).