I've never met someone who complained about having too much well-run structured cabling.
In your drawings (with the green room at the S-E corner), if you have some space that you could dedicate to a small network closet in the green room that would be great. There are always cheap four-post racks on craigslist that you could use to mount your PA equipment, your network gear, etc.
Something like this: https://philadelphia.craigslist.org/sys/d/fairless-hills-42u-tripp-lite-server/6827706454.html
Or this: https://southjersey.craigslist.org/sop/d/shiloh-apc-open-frame-server-rack/6820659150.htm
The benefit of a four-post rack is that it doesn't generally need to be anchored to the ground (still nice if you can though), whereas a two-poster NEEDS to be bolted to the floor.
After you've picked your preferred location for your network closet, you need to run home-runs to all your remote drops. This is when you want a helper, and ideally several boxes of bulk cable. If you're running six homeruns to each termination, buying three boxes of 1000' of cat5e means you only have to pull cable twice per termination (pulling three cables and routing them is just as easy as pulling one). If you have the budget to buy six boxes of cable, then you'll be even better off and you only have to do one pull per termination. Cable is cheap, terminations are cheap, boxes are cheap, and if you're doing it on your own time, then the labor is all you'll care about and you can add more drops to the ceiling grid over time.
Since this will be an overall structured cabling plan, some things you can do:
Six ethernet runs to each corner of the theater terminating and labelled as 1A-1F through 4A-4F
Six runs to each corner of the ceiling grid (you'll want these eventually, might as well plan to put them in now), labelled as 5A-5F through 8A-8F
Use some of your leftover ethernet cabling to run to the grid above your common stage locations to have two XLR jacks that you can use for overhead mics. You can solder an XLR jack to the end of ethernet cabling, just use two of the ethernet strands per xlr pin. Overhead XLR that you can run to a rack-mounted Behringer XR18 that lives in your network rack would be pretty sweet. Another option is soldering up your own little patch cables that have a male Ethernet jack and a (female or male) XLR jack and then you can use any of your homeruns to send mic-level or line-level audio back to a rack-mounted mixer.
You could also buy some two-conductor speaker wire and terminate to speakons up in the grid, and home-run them back to the network rack. I'd keep the speaker wire a few inches away from the low-voltage cabling if you can. The ability to fly a speaker, plug in to a connector 10 feet away and then just patch in the rack is NICE. You could also run to speakons that terminate in the corners of your black box instead of the grid if you want to run through the crawl space, but I'd generally prefer to fly the speakers if you can get away with it. You can always send line-level audio through your low-voltage runs to get to a powered speaker or sub in any of your corners anyway.
When you're planning and laying out your rack, from top to bottom I'd plan for:
Ethernet switch
Etnernet terminations for your patch panel(s). These need to be WELL labelled
Special purpose terminations for your audio gear (your XLR terminated ethernet runs)
Rack mounted mixing rig
Special purpose audio gear
Lighting control
Power distribution (rack-mounted power bar to power all your gear)
Open space for future expansion
Power amplifiers
Audio connectors for speakers