There's no way to use the wheel as anything but standing. Also whatever it sits on can't be higher than the plastic base top level or it catches the top of the cage (so a shelf in the bars is a no go) and it will definitely need to be a platform so I can control the height accurately enough.
If I make my own I can just set the legs in from the edge at the back so that the taper of the base isn't an issue. I'll just use some kiln-dried solid spruce shelving for this (sanded of course, and untreated).
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Is there any reason tot to use screws when joining items together...I could use small screws for the platform to screen into dowel or square section legs?
What material do you have that I can see 'surfacing' your platforms and ledges. Looks like a matting of some sort.
As for the tubes...none of the reviews suggest they're too small for Syrian and all say they've used them to replace tubes that come with Syrian Hamster cages so hopefully they're ok....I measure the opening of them as being 7cm. Can hamsters climb a very short vertical section, or do they need to be angled?
Lastly with the plaza cage, since you're familiar, how important is a section of bedding that comes up above the level of the plastic base? The base by my reckoning gives around a 6 inch bedding depth (maybe a smidge less) so is it very important to have a section that is deeper than this? I could ramp the bedding up to a platform to give a portion that is deeper (and use some kind of matting around the bars to prevent spillage) but obviously would need deconstructing if ever needing to take the top of the cage off as opposed to just accessing through the doors. That approach would reduce flat cage floor space for toys but obviously create a deep bedding area for tunnelling.
Oh, and having built the cage, in my opinion the door is 'loose' on one side...assumedly just bend the catch down a fraction with some needle nose pliars to firm it up?