Little update in case someone encounters the same issue...
It seems the space stab holes are mounted ever so slightly too close to each other, or, the wire i've got was ever so slightly too long (as i've correctly guessed initially). This then causes the stab stems to rub against the edge of the stabilizer housing (the wire displaces the bottom too far to the left on the left stab and too far to the right on the right stab - since the stems can pivot around the wire, this forces the stems to rub against the right and left wall of the housing respectively).
While i was troubleshooting, i first tried lightly shaving off some material off the moving part of the stabilizer under the stem with an emery file. Bad idea. It leaves a sandpapery feel to the stabilizer that i had to smooth with sandpaper, and it all amounted to nothing.
What did help was removing the stab wire (you don't need to remove the plate or desolder anything to do that, it's accessible through the hole and on the side - if you need to do this and can't figure it out, let me know, i'll help), take the pliers and lightly bend the short segments *inwards*, like this:
/_______\
And by *lightly*, i mean really lightly. It's a trial and error thing. You bend it a little, put it back, mount a space bar cap, try it, remove it, remove the wire, bend a little more etc. until it's just right.
I'm getting 0 stickyness now and the sandpaper texture is irrelevant, as the stem isn't chafing the edge of the housing anymore anyways.
