How to run speaker wires?

I released the boot from the sheetmetal on both sides and fished it through.

The vac line comes through the firewall to the left of the passenger footwell, up and behind the heater core/vent assembly box.
You might have to pull back the top edge of the carpet in that area to see it.

any procedures on releasing the boot or should it just pop off?

At both ends, the boot is just pushed into the metal and retained like a grommet. Use a blunt flat edge object between the metal and the boot and work that around the perimeter while prying gently back until it releases.
Re-installation is easier if you use some silicone grease around the lip of the boot. On the door side, you can reach in and pull it back into place (it has a tab) while pushing from the outside but i don't remember if you can pull it from within on the body side.

Boot comes out like a charm. After about an hour and some bloody hands, I was finally able to fish a coat hanger through the boot. I admire this community because everyone makes these jobs sound so easy but I promise owning this car is being in an abusive love-hate relationship, and that’s what makes this car what it is. Anyway, I really have no idea how I am going to fit the wire through the boot along with the coat hanger because there just seems to not be any clearance and I’m dreading thinking about it haha

To be a Z31 enthusiast, you have to be equal parts ingenious cheapskate and automotive sadist.

I was able to fish some relatively large 8mm dia, 4 16awg conductor PVC jacketed speaker wire through mine when i upgraded my speakers to some 2-way 6.5" speakers.
The crossovers are tucked up around the side ducts beneath the dash. I used some pro audio stuff left over from a media center install my buddy did, similar to this stuff

Finished routing 3/4 of the speakers now on to the final one which happens to be the passenger side door speaker, which so far looks like I’m only going to be successful based on luck lol. What a job those other ones were man. Also wondering, where can I fit some 8 gauge power wire through the firewall to power my amplifier? Can’t seem to find any crevices and may end up just drilling a hole. In addition to this, can I use the same 8 gauge wire that comes in the amp wiring kit as a ground wire? The ground cable that comes with it is only 3 feet, and I’m not sure what to ground it on. I’m running the new amplifier under the passenger seat next to the stock one. Should the stock one be unplugged when I run this new one?

About the sadist part, i ran mine through the wiring loom boot that is used for the factory harness that passes thru behind/beneath the battery as i wasn't keen on drilling though the firewall.

There is a passthru grommet for the hvac vacuum line that you could probably use, on the engine side it's near where the heater core lines pass thru. It can be a pain to get to on the other side tho.

I'm not a professional but know enough to be a bit "detail oriented" when it comes to wiring. I used to make process equipment chassis wiring harnesses as part of my job.

I ran two 8awg wires, one power and one ground, but also grounded to the chassis at the mounting point. The 12v+ is fused at the battery and a fuse block at the amps. I have 2 amps and a sound processor in the hatch compartment behind the seats tied into the fuse block..

Yeah, I would remove the factory amp and use it's sheet-metal screw mounting points as a point for a ground ring terminal.

Is it safe to use the metal support bar that runs across under the dash as a ground? There’s bolts on there that almost seem to be specific grounding points

I’m also not totally sure what to use as a ground wire for my head unit. The aftermarket head unit comes with a small harness plug with the 12v power ground antenna etc. wires to be soldered to the stock harness in the Z. However, the stock harness doesn’t have a ground wire. I have some 16 gauge car wire stuff I’m using for the amp remote cable I picked up at Walmart but it’s thicker than the black ground wire on the aftermarket head unit harness not sure if this would be a problem or not but would like to make sure before I attempt to ground it

Any solid point on the chassis should be good. If it has paint on it, scrape it to bare metal for the best contact.

You can also use a internal/external tooth washer for a more secure and electrically conductive mount and thicker wire won't be a problem for ground.

Also, as far as the stock harness goes, don't attempt to patch the factory dimmable lighting circuit into your head unit for controlling any sort of dimmer function. It can cause shorting in both as i think the car uses a variable ground signal for dimming and most aftermarket head units I've encountered need a variable +12v signal. I mostly remember that they are rarely compatible.