Thank you for the comprehensive response.
You're welcome, and sorry for the super-late reply here.
But overall, do you think the subsequent health issues were more likely caused by the treatment regime than water parameters?
It could be both. If you are serious about quarantine (and it seems like you are), the investment into higher-grade testing equipment will help reduce the inherent risks of quarantining. The Hanna high-range ammonia checker and copper checker will help you understand the answer to this question. There is simply too much potential variability in results with the "drop and eyeball" method of the API kits.
As the copper treatment elevates the nitrate/nitrate levels, how do I know if the nitrates/nitrates are actually too high?
Ammonia and copper levels will be the most important parameters you are measuring here. Hanna (high-range Nitrate) would also be my go-to for Nitrate testing. I have this checker, but have never tested nitrates in my fish quarantine. It would be a good idea, however to have an idea of what the levels are - and being able to mark trends between the fishes appetites (as far as I'm concerned, the biggest obstacle with an aggressive prophylactic protocol) and nitrate levels.
I use SJ Wave ammonia test strips.
...See above...
Below is a list of the fish I tried to QT. They were all quite small, and I made three towers of PVC tubing to create plenty of hiding spots.
PVC is great for hiding spots, and conducive to the 'sterile-like' environment we are trying to create. It's best advantage is ability to clean/sterilize easily. I use a fake coral insert in mine, and (admittedly) increase risk for vanity's sake....
The filter is a Seachem Tidal Filter 35, with sponge and bio media. Plus another sponge filter and an air stone.
Should be fine assuming it has cycled, although I stand by the bio-wheel technology with respect to killing ammonia. I literally have never tested for ammonia in my QT's once the biological filtration is established, despite the relative high number of fish I QT at a time or the enormous amount that I feed the tank. I literally dump food in the tank (see above comment on fish appetite...)
The fish appeared quite healthy when they arrived. I ordered the fish, so didn't get to see them in the store.
This is the biggest step you can take to minimize attrition in your QT. Almost every fish I have lost during the QT process, I started with an underweight, sick, or wounded fish. If I purchase online, I generally stick with Divers Den livestock - they have always been healthy, and usually will eat immediately - even after a relatively quick acclimation to 2.0 - 2.3 ppm copper levels. Also keep in mind that copper (especially when compounded with other meds) will reduce the fish's appetite - if you start with a fat fish, even if they refuse to eat the duration of treatment (14 days for me) you will not have to worry about them dying from starvation.
I used copper safe straight away, as I got an ich outbreak from this same vendor previously. I use API copper test to confirm the copper level.
Makes sense, and this is my protocol as well, although I to try to introduce fish at 1ppm, and increase the copper level to 2.0 over a 24 hour period.
Any additional thoughts/theories/suggestions?
I do agree with other posters, that 20 fish is too many fish to try to quarantine at a go in such a small tank but I believe it was likely much more than this factor alone that led to the fish mortality you saw. If you are only using copper, keep in mind there are many diseases that it will not treat alone. FWIW, I combine copper, metronidozole, and praziquantil treatment, simultaneously - this will cure (external) uronema, velvet, ich, brook, and most flukes which I would attribute ~ 99% of the mortality to that we see in most fish and systems. Minimizing the number of fish you start with will keep aggression/stress to a minimum, minimize the amount of food you will need to feed, and minimize the chance that a pathogen (not treatable by copper alone) will impact other fish. If 1 fish is in QT, then only 1 animal is at risk - if there are 20 then you risk losing all 20.
Get yourself some Hanna checkers for Copper, Ammonia, Nitrate - this will help you accurately troubleshoot when things go awry.