I agree that PA28 fuel systems are not complex compared to some, but I don't consider the tank switch/tap an example of good ergonomic design.
To some extent that's a function of the times, ergonomics and human factors weren't really thought about back then, and there are many examples of even worse systems! However it's my view that, as much as you can try and 'train out' the designed-in flaws, they can still affect the outcome of an unexpected event; this may be an example.
To whit; objects have affordances; a door handle is directly visible and affords pulling on it, a door plate affords pushing on it. A PA38, or even a 172 fuel tap is directly visible to the pilot (IIRC?), and they point laterally to the fuel tank in question. On the other hand the PA28 tap is not especially visible, it is awkward to operate, and the longitudinal operation doesn't easily relate to the tank you're operating on, or have been operating on.
So, in the event of an 'oh sh*t' moment, and while you'd hope training will kick in and you do everything right, something that's not especially visible and doesn't tell you what it's doing (ie. which tank it's pointing to) doesn't exactly put itself out there for you to attend to with the limited processing you're likely to have at that time. OTOH the pressure gauge and pump switch are more line of sight, and so may be less likely to be missed. Having said that you've then got the issue, especially in this part of the world, of which way the switch should be when it's ON! Then there's the gauge which is doesn't exactly stand out from the others...
Now, like you I haven't flown one of these in quite a while but the drill is very clearly loud in my head and I'd like to think the fuel tank switch would be within one of the first few things I did (after carb heat, mix, pump), yet I've been fortunate and I've not needed to do this in anger - at least not in a PA28 - and so I've not been tested for real. This pilot was tested, and she's berated herself for not following the drill, and while I don't think the PA28 fuel switch design excuses that, it could perhaps explain it to a certain extent (along with other things discussed in the audio).
Where I'm heading with this is, what could we as pilots or instructors do to counter this? Mnemonics and memory training are all very well, but in the heat of the moment is there something that would assist us to get things right? With some of the 'planes I flew we had a QRH goto just for such an event, but in this era of inexpensive electronics I wonder if there's a place for a 'big red button' that you hit following which a voice starts telling you the drill, or it's put up on a screen?
I put this explanation and these ideas up as points for discussion and 'what can we learn' from this event in order to improve what we do now and in the future, and to - hopefully - reduce the likelihood of it happening again. That Michelle has been direct and truthful about what happened assists us all in this, but I think but we actually need to do something with that information for it to be effective.
FP.