I know how you feel
I bought an 80 x 50 cage for Charlie and it seemed huge and I loved the front opening door (Savic Mickey 2XL) and it wasn't too high so no worries about fall risks (38cm high). But - the low height caused issues with wheel sizes and substrate depth, and the cage never seemed quite big enough. But I did love it and just kept wishing it was 2" taller, 100cm instead of 80cm and with a 25cm clear base lol! Or even just wider and taller with the standard base. The 7mm bar spacing does make it harder for them to bar chew, but not impossible. Charlie went through a short spate of it after a big change when we went away on holiday for 10 days. Luckily it stopped after a couple of weeks of ignoring and going to bed early.
Maybe if the platform is an issue - being noisy and not particularly stable perhaps, it might be better to leave it out. Hammies do get stressed if something major gets taken out of the cage or the layout changes significantly sometimes. I found it a lot when Charlie was younger - he accepts a bit of change better now he's older but I tend to do it when he's out of sight and hearing or he gets stressed hearing me doing things to the cage! So he just gets the finished result.
If you're wanting to upgrade though, you could maybe get some money back by selling the Alaska after getting something else. Although because they're only £33 ish new it probably won't go for more than £20 but it's still £20 towards another cage rather than spending more money on platforms etc to get the Alaska right. I ended up going for a large flat roofed house instead of a platform when my plastic one got too annoying and the ladder broke! But the cage was lower so less of a drop onto the house roof.
How about a detolf? No bar chewing. Only costs £40 (although you need bits of wood and mesh to make a lid). From the sound of your hammy I'm not sure a Zoozone would be right for him. They have good floor area but not much height for levels and he sounds like an active energetic climby kind of hammy! With a detolf you wouldn't have bars to be chewed like in a cage, and the extra floor area would make up for not having higher levels.
For now just try and make his Alaska cosy. Stick with the shelf and maybe prop it up underneath with something so it doesn't wobble so much. Give him lots of substrate and plenty of hidey places - small cardboard boxes would do, so he doesn't feel exposed and to add a bit of interest. And maybe save up a bit and daydream about the ideal cage!