I ended up getting a free Sunday morning so I did go to Zia, with a Scottish colleague whose interest was piqued. Two locations: the Bethany shop and the one on Thunderbird.
A funny trip, and a slice of life.
I had to travel from North Scottsdale, which is a long trip, despite the deceptive maps, which I've now realised show not blocks but geometric square areas of development, each containing hundreds of blocks. The Uber driver on the way to the Bethany Zia, which I'm told was in "Maryvale" (one of the only areas of Phoenix that seemed to have a name that was in use) made sure to warn me that it was in a "terrible neighbourhood", that I needed to keep my eyes open for trouble, and then asked whether I was "packing a piece", I assume as a joke. The shop was next to a Walmart, so we went in (good for gifts, and Walmarts are exotic and exciting Americana to Brits). The check out staff, when they heard our accents and had all come and shaken our hands(!), advised us very kindly that "this is a really bad area, and you should make sure you leave as soon as possible". The Bethany Zia had a shabby and rather fraught feel to it, but the staff were lovely and it had some cool stuff in it, including lots of underpriced jazz funk / Gilles Peterson-friendly stuff that would have been six times the price in London. Weirdly, it also has a large selection of Ogun records, by the likes of Elton Dean and Mike Osborne, as well as some Soft Machine-adjacent rock records. No idea how those had got there - I've never seen that sort of thing even in the UK. Security was tight and you had to be walked in and out of the shop to ensure nothing was stolen.
The Thunderbird Zia was night and day in contrast. Clean, and thronged with happy customers, some with their children, and with a great selection of other (non-musical) stuff like books, old mags, and the like.
Anyway, I found some great stuff in both, including a few things that I had been looking for over a few years but had never found at the right price point to justify Discogs.
Neither of the shops was a jazz specialist, but they had generous shelf space set aside for it, equal to the entire stock of many London record shops.
As always, record-shopping in a foreign city is a great way to explore it. And I didn't even have to wear that gun.