Success! The HV programmer worked like a charm! For only about three Euro of additional components I threw together the basic design, replacing components where necessary (my local shop doesn’t sell microchips, as online stores has made that highly impractical for the owner). The biggest thing missing, though, was a DC jack that could be mounted on the perfboard. so, I’ll have to fumble some solution to work for my setup.
In any case, a quick upload to the ATtiny13 I’m using as HV programmer, and a quick reset of the ATtiny84 later, and the reset disable fuse is reset again! It felt amazing building my own tool to repair an issue I ran into, even if I did essentially assemble somebody else’s work.
I set to work retooling it to put on perfboard, as I’m sure this won’t be the last time fuses get screwed up. Instead of making separate reprogrammers per 8 or 14-pin chip, I figured to combine the two in one:

I then used KiCAD PCBNEW setup at a grid of 2.54mm with 1mm trace width to plan out my perfboard:

The green lines denote the back of the perfboard, and my intention is to have those be solder lines, where the red lines are jumpers on the top of the board. I’m curious to see whether that one near the LED will interfere with it too much. I’ll be testing a method to guide my solder bridges on the back using a stripped copper wire as a guide. I hope to give it a good test tomorrow to see how it works out.