I'm not sure why but I was imagining a tall tank

. I agree with Beryl though. However, you might be able to make it work as a temporary solution to prevent escapes if you could create a full level rather than shelves. The floorspace is quite a bit smaller than her current tank so she is likely to bar chew.
I wouldn't move her in it tonight as there are fall risks. They can behave like lemmings and jump off top shelves or climb the bars to the roof and monkey bar across the roof (usually looking for a way out) and then just drop and can bounce off the edge of shelves on the way down or land on something.
If you can make the tank lid as secure as possible for tonight and hamsterproof the room. I would think this cage could be adapted with a bit more time on it - as a temporary home to give you some breathing space.
What you'd need probably is
1) About 10" high cardboard all round the inside bars (you can attach with cable ties) and fill that up with bedding so it's about 12" of bedding. This effectively reduces the height (although not enough) and means she can dig tunnels and a burrow which might keep her happy enough in the cage size for now.
2) Use two of the current shelves on the same level and put a piece of wood or something across to make a solid level about 40cm about the top of the final substrate height. So it's like a roof that she can't get up to or above (ie remove the ladders). The third shelf can be used below this just as a normal shelf for her lowered cage.
This does mean you lose the top part of the cage because it would take a bit more diy to create a secure full level with access up to it so there's like a second floor of the cage.
It's not so much the volume of the cage that they need for size. But more floor level and less height. To be honest they only really climb to see if they can get out! And it would be risky. You might get away with it with 12" of bedding and nothing to land on (ie any cage items under shelves) but still risky.
Re the wheel - if that's the only wheel you have for now, you could maybe cut a strip of cardboard to stick over the mesh running surface. Wire wheels have been a no no for some time even though they are still sold unfortunately - due to the number of injuries and painful feet conditions caused.
As a permanent cage, the floor area is unlikely to be big enough for a female syrian - it's not far off! Something like 40" by 19" to 20" is about the minimum floor area you want with a cage height of 20" to 24" max.