I wouldn't try the upside down thing with the Trixie wheel! Nice thought CMB - when I tried it, the wheel kept falling off the stand. Although my other Trixie wheel was impossible to get the stand off - but it is not secured in any way like the wodent wheel is. It probably wouldn't fit above the shelf if on the stand either.
Lilac dreams I do remember someone on here who had the Trixie wheel above the shelf, with the shelf on the lowest setting. I was never quite sure how it was fixed on but I remember it was a tight squeeze and then she had to give up because it started wobbling.
It's something that has always been tricky about the Alexander - where to put the wheel and keep the nice racetrack 3 shelves. If you take one of the shelves out it basically becomes a taller Barney and you lose the advantage of the three shelves.
If it helps I spent a lot of time working out set ups for an Alexander! Far too much time.
I had two options to have both a large Syrian wheel and a deep digging area.
The first option was to have the wheel centre back, as it sounds like you had before - meaning the substrate there can't be too deep. And then on one end of the cage, under the shelf, fence off the whole width of the cage with a 20cm high bendy stick bridge (so the bridge is just under the shelf and can't be fallen on. Then fill that section very deep with substrate - makes a kind of 15 to 18cm wide, long digging area. I had thought to put cardboard inside the bars round that area to hold the substrate in, but I've found with the 7mm bar spacing you can have it really deep up against the bars and it doesn't fall out.
Another option was to have the wheel under the left hand shelf with the left hand shelf quite high up over it and the other big shelf lower down, with the middle section sloping down between the two - ie split level shelves with a sloping joining platform.
Again the wheel area would need to be low substrate but you could heap it up in the middle of the cage in a big mountain. An alternative version of that option was still have the wheel under the shelf but instead of along the end wall. along the back wall near the left corner (so it's partly under the longer shelf and partly under the joining middle shelf). Then have a digging boxor digging area in the front left corner opposite.
I have another option I would do now if I had an Alexander, but it would mean buying a new wheel. I currently have the 12" Silent Runner (the orange one with the big kidney shaped holes). It is well made and comes with a sturdy metal stand but you can also buy a separate cage mounting kit for about £5 which works very well and keeps the wheel sturdy and stable. Although the Silent Runner would be too tall (35cm tall) on its stand (due to the sloping roof) - if it was screwed to the bars without the stand, the wheel itself would only be 12" (30cm) tall - you could screw it to the bars as high as it would go to make the most of the substrate underneath - although it would still be quite low in that area. At the centre back of the Alexander, between the two long shelves. Although TBH it's not much different from having a Trixie wheel in that position on its stand. You might gain a couple of cm of substrate under the wheel. And again have digging area at one end of the Alexander under the shelves.
I too think the shelves are important in that cage - they provide virtually a full extra level to run around on and lots of shelter under the shelves.
Now I've had the Barney, I think it could work just sloping the substrate up from the centre to one end with it deep at the end of the cage to make a deep area, without fencing it off and it shouldn't fall out of the bars - or you could put cardboard round.
If you were feeling really ambitious you could try another idea I never followed through
Which is to stick perspex around the top of the cage base about 20cm high all round, stick u channels to the top of the perspex and sit the cage in the u channels - giving you a 35 cm (ish) deep base to fill with substrate and still keep the shelves in their normal position (and the wheel centre back).
It actually was going to work out rather expensive in perspex though.
It would look something like this one
https://www.amazon.co.uk/Imac-Plexi-.../dp/B00O4B50N8
Or there's this idea (3rd photo down)
Which is just a melamine deep base with the bars on top (sat in u channels). Only downside is you can't see the tunnels if they dig tunnels in the deep substrate. But I guess you could have three sides melamine and one side perspex.
Naturnahe Hamstergehege: Bautipps - DIY tips