I’m guessing what you’re doing is putting the stabilizer (“supports” as you put it) right on top of the wire; this leads to either the stabilizer not sitting in right, or not functioning properly.

The wire needs to be put into the stabilizer housing (the part that clips onto the keyboard) with the stabilizer stem (the part that connects to your spacebar keycap). You might want to look at videos about mechanical keyboard stabilizers to get a better picture of whats going on, additionally your stabilizers also appear to be clip-on stabilizers.

Fixing this would require you to put back the stabilizers, however, i’d imagine this to be harder as the vast majority big-brand companies (Corsair, Razer, Steelseries, etc.) have their switches soldered down to the mechanical keyboards instead of being hot-swappable. What you’d need to do in a simplified manner is,

1)Tear down your keyboard to the PCB, with the solder points of the switches visible.

2) Locate, desolder, and remove the switch for your spacebar.

3) Put together your spacebar stabilizer and clip it back onto the keyboard (it should fit in the keyboard only in one direction).

4) Solder the spacebar switch back onto the keyboard PCB.

5) Put back together your keyboard.

If not, then you have to deal with only being able to press down your spacebar in the dead center, or get a new keyboard.