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As a last resort you could get an RF shielding enclosure like this. It has the added advantage that you can camp out in it at gigs. https://www.vtechtextiles.com/rf-emi-shielding-enclosures-tents/

Very tempting indeed. I wonder why they made the pickup on the Squier a tiny bit smaller than a regular Mustang pup? To make upgrades less straightforward I guess lol! Or are they in the same sized casing but just spaced slightly differently? Comparison pic below (Fender Vintera on the left and Squier on the right).

The compensated nut is much wider than the old SR nut so it definitely wouldn't be a drop-in replacement.

If you're up for building it yourself here's a circuit for a mid control. This has sweepable freq (160 - 1kHz) but, as ITU says, you could replace the dual gang pot (P2A / P2B in the schematic) with a switch and two trimmers (or perhaps two dual gang mini pots in this case) to select your chosen mid frequencies. http://www.redcircuits.com/Page168.htm It might be simpler to just swap out the existing preamp for a three-band with switchable mids! Eg. Aguilar OBP-3, Bartolini HR 2.4 AP/918 and others.

John East does a mid control (with variable freq sweep) that functions as a stand alone unit. I don't see why that couldn't be run either before or after your existing 2-band using the same power supply. Have a chat with John and I'm sure he'll sort you out.

Afraid not, the lack of open notes dampened my enthusiasm a bit! A retrofit takes them about 6-8 weeks to turn round from what I understand but I'm not exactly sure what it involves.

I contacted FretTrax last year about the open note issue (I asked I if it would work with a zero fret), here's their reply: "Thanks for getting in touch and for your question. I get that question a lot but unfortunately the answer is 'no' - a zero fret doesn't help at all. I already know, without a zero fret, when a string is open - a string is open if it's not fretted (that's how I turn off a previously fretted note). So, I could turn on open notes easily without a zero fret - the issue is knowing when NOT to turn them on and when to turn them off. Otherwise, every open string would ring all the time unless you have a mechanism to SELECTIVELY turn on/off open notes. And, that mechanism is 'pluck detect' where a right hand pluck triggers a note - and that note can be open or fretted. That feature is in the works and then FretTraX will have opens, velocity, etc. All the videos were done with fretted notes only. Some pretty wild things can be accomplished. But, when we add pluck detect (still quite a ways away), things will get even wilder!"

The pickup is attached to the pickguard using two machine screws which screw into the flatwork of the pup with a spring in between (like a Strat). The screws are not the same as regular P or J screws which tap into the bodywork. Here's a pic of my old Musicmaster which had the later pickguard shape, same as yours.

The Burns website lists the current Marquee reissue model as a 34", was the vintage original a 32"? http://www.burnsguitars.com/marqueebass.php

My Hofner Club is 6lbs 10oz with a centre block so an Ignition is a good call being fully hollow.

Excellent!

It seems reasonable to suppose that white and red will be the hot wires, in which case yes you will be wired in series. Best thing is to give it a go and see how it sounds.

I've not used GHS contact core strings with a piezo but I have a tapered B string which works fine with my piezo bridge. The piezo picks up vibrations from the string and will work fine whether they're regular or tapered.

The white and red wires will be hot, black will be cold. Typically speaking you'd wire them in series by joining the red wire (hot) from one coil with the black wire (cold) from the other. White (hot) will then go to the vol pot and the remaining black (cold) to ground.

Hmm, that's a bit odd. Guitar parts with 6-32 thread are usually UNC to fit vintage Fender.