Turns out I was lucky and my nudging
only pushed the roller guide arm off the roller guide. It was already in tension, hence the disappearing act. I managed to disassemble the whole unit, flipped it upside down, and reattached the arm to the roller guide.
Something I noticed after fixing the issue, was that the roller guide was very wobbly. I don't remember if it used to be like this. Probably not, since my VHS-C tracking became abysmal, which was not the case before my tinkering.
I had to manually fix the tracking, playback works like a charm now.
I also took the opportunity to clean the head with 97+ ISO. I found that lens cleaning swabs work like a charm for cleaning video heads, no snagging at all, no damage. All in all, a very finnicky 6-head Sony VCR, I must say.