While I'm aware that my priorities are messed up to the point of being silly
Nope - they are what they are. Not silly in the least. Everybody makes their own requirements list.
I'm more willing to either wait, put in some work and/ or give up some functionality, to have either a proprietary network-less solution or an open source networked one.
I would love to hear how you do all that LAN-only for 500 bucks in gear that is accurate enough for you...and that works as a turnkey solution that doesn't require a lot of hardware maintenance.
FWIW, my PurpleAir phones home too, although I don't know if it will work if I block it outbound at the router. I know it functions for some period of time during Internet outages, but I never tried to power-reset it at one of those rare times to know either way.
There have been guys who have posted totally rolled-their-own things from grabbing a bunch of sensors and doing all the software themselves, but I didn't go that way since there's a time-value of your labor too, unless building something yourself is the adventure in itself.
I still like a Vue plus serial/usb datalogger as the lowest price to get a quality station supported by a good vendor that works weewx and LAN-only, but many people here speak badly of the Vue due to its limitations vs. the VP2 (one sensor suite, less expandable, less maintainable, etc.), but that doesn't hit your AQI/lightning/light sensor requirements at all.
(FWIW - I got my VP2 just as the Vue was coming out, so I didn't go Vue then because it was too new. I also hit a fabulous deal of $400 for the station and $100 for the serial datalogger, so I hit your $500 line back in early 2009 for that setup.)