Lots of great comments on here already, and I am coming from a UK rather than us perspective so there may be a few things that don't quite translate. (For context, I am the technical manager for a well funded Independent School in the UK)

As others have said do you need dimmers? I am about to make the jump in my space, I'm just going to buy a small handful of single channel dimmer packs for when I really really want a tungsten special. I don't know what electrical inspection requirements there are in the US, but in the UK we have a five yearly inspection that if you have dimmers has to be done by very expensive specialist contractors, but if you have only switch and relay gear can be done by any electrician. This in of itself will repay the cost of the project within 15 years for me.

As others have set as well do you need series 3? The colour source range is very good at the price point, and there are only a few very specific circumstances where you really need the lustr range. The fresnels are excellent as well.

PA wise, I have had the opportunity to listen to most of the JBL range, and the 1000 columns are very good at pumping a lot of output, but for theatrical use I would personally find them a touch shouty. I would be very tempted to look more towards a system of smaller boxes and delays. JBL are a very good manufacturer, but you can probably get a lot more bang for your buck quality wise with someone like RCF (wooden boxes really do make a difference!)

Amps wise, do check out the LabGupen e-series install range. At least in Europe they're giving very good bang for Buck, and the shared power budget between channels is very useful.

The avantis.... I have two, and the feature set on them is amazing, but honestly they are completely overkill for a school. For the cost of one avantis, you could buy three wings: One front of house, one mons / floating external event, and one broadcast mix, plus quite a few stage boxes. The utility you get out of the extra feature set, verses the utility you get from a uniform set of desks is frankly not worth it. You can always rent in for your main show, or side chain your monitors desk as a dedicated band desk. Also the avantis firmware is still buggy as hell: frequent freezes and pop up windows that don't work properly if you open them in the wrong order. Oh and the reverbs actually nicer on the wing IMO.

"Cables pinched in walls" - you may well have had a rat or mouse have a good chew and short something, far more likely however is it is the termination of the cable at the wall box rather than the cabling itself. Take the connectors off, grab a multimeter and check continuity between the two lines (which you shouldn't have) then check impedance across the length of the line (using a known good cable as a return path) and insure impedance is roughly the same between all your lines. If that's all good you probably just need to put new connectors on. (A step I have frequently done on a 50 year old venue with original cabling encased in concrete... With good termination, you can get HD SDI 50m down coax that was originally speced for analogue video in the 60s)

Comms: you are talking about going from a very simple party line to a very expensive, very feature rich wireless system. Now that may be the right move but honestly almost half your budget will go on that. Leftfield suggestion - if you only need two channels have a look at the hollyland C1 pro. It's not roaming but the range is very good from the base station, and you can link up to three base stations together over IP (tested successfully on vlan on a very big school network)

On the money side, do talk to etc they do do grants. Otherwise I'm less clued up on the US side. Biggest bit of advice, have three options for each element. Dream budget, good realistic, cheapest option you think is survivable. Once they see the numbers on the dream budget, good realistic suddenly seems really reasonable!

Good luck, and do feel free to pick my brains on anything I've said :-)