Hello - he will be much better in the hamster heaven, and glad you've removed the tubes and penthouse - he'll be able to develop normal behaviours more easily and less stressful changes needed (as usually the tubes get blocked up etc).
I would add the new wheel at the same time. The small ones they come with are far too small and can cause back problems and pain and if it's uncomfortable to use also he may just stop using it and start bar chewing instead!
The Trixie 28cm wheel is fine and not too expensive. Yes the substrate will need to be a bit lower in the wheel area due to the height of the cage only being about 36cm internally - I just "sloped" it away from there so it was deeper in the rest of the cage. On the plus side the height of the cage means there is less danger of fall risks and also you can attach things to the top bars due to it having a nice big front opening door - which really helps with interaction with the hamster.
When moving him across I find a transition day helps them settle much quicker. So put substrate in the new cage and add the new toys and maybe one of his old toys and pop him in there to explore and play in it. If he freaks out and wants to come out again, pop him back in his old cage and try again the next day. Second time he should be more interested and exploring. Make it interesting to explore so semi set up with at least 3" to 4" deep of new substrate in. If he seems happy exploring the first time then fine, leave him in for a play and explore. Then put him back in his old cage.
Then the day after the exploring session (during which time his scent will be in the new cage), move everything over. As the new cage has a bigger floor area, you can leave the new substrate in and spread the old substrate on top of it - you want at least 3 to 4" - I used to virtually fill the base - so about 5" - it helps cushion any falls and gives them the option to dig and mess about with the substrate - they sometimes like pushing it into piles and burying things in it.
Move his nest across as well and a bit of his old hoard if it's under the nest. And put a big pile of new nesting material out as well. Torn up strips of plain white toilet paper are best and safest - not in the house, just a pile in the cage somewhere and he'll take some to refurbish his nest or build a new one. Sometimes they pouch it to take to the nest.
Scattering some food on the substrate helps distract them as well and hiding the odd treat (especially in the house you want them to use). It's then a bit like starting from scratch with settling in. Leave him alone for 2 or 3 days - just talk throgh the bars - unless he shows he wants to come out. He may be a bit skitty at first. It can take two weeks for them to fully settle in the new cage, although I find doing the transition speeds that up a lot. But don't clean anything in the first two weeks, just spot clean the pee every 2 or 3 days, or empty the litter tray every few days if he's using that.
You could maybe keep the solid shelf and take the other one out - you need to take one of them out to fit a 28cm wheel in.
Houses are quite important. They like to build really big cosy nests and if the house isn't big enough they may ignore it and build an open nest under a shelf. When I had that solid shelf with the little pod house on, our hamster decided to nest in the pod house and it was a complete nightmare as it wasn't big enough and got sweaty and smelly inside being plastic. And he stuffed it so full the top kept popping off, so I ended up removing it and giving him a bigger house at floor level.
The main thing with a house is that it is open underneath and sat on top of the substrate, so they can burrow down to keep warm and bury hoards under their nest. Most people use wood or cardboard houses. It needs to be dark inside -they need somewhere dark to go to to feel secure. Putting a bendy stick bridge over the door helps make it dark inside and adds a "tunnel" entrance so they're more likely to use it.
Smooth Wood houses do need painting with plastikote inside though so they're wipe clean or they can get stinky. A child's shoe box can make a good cardboard box house. Cut the base out and use the lid as a lift off roof so you can check inside without the nest falling apart and cut a door at one end of the long side for an entrance - they tend to nest furthest away from the door where it's darker.
Rodipet make amazing hamster houses but they're not cheap - some have a piece of granite tile for the roof which is good for putting a food bowl on and it helps keep their nails shortened every time they go to get food (rough granite).
To be honest I think that cage works best without the shelves and with a good sized flat roofed house instead of a shelf. It's almost impossible to fit a house under the shelf and once the wheel is in as well it's hard to fit a decent sized house in - but not impossible - depends on which house you get. I had a flat roofed house instead of a shelf and then had smaller screw in shelf or two just over the house - a lava ledge eg and also a hanging rat sputnik - those are great but quite big in the cage. It gives them something to sit under and with that cage they can climb into it from floor level.
I'll add a picture of my layout in that cage a few years ago.
Toys - they're not that interested in toys really - unless it's edible or something to hide in - so floor tunnels, hidey places etc work well. The seesaw would be fine as long as it's not to narrow - they can get stuck in narrow tubes. So they need plenty of "enrichment" and that includes, enough substrate, places to go and things to do - eg a bit of variety - a level to climb onto (but don't get those hanging ladders, they're dangerous). Lots of floor toys like tunnels and hidey places, the odd thing attached to the bars eg.
Most toys sold for hamsters are really too small or dangerous. They're designed for little dwarf hamsters. Syrians do better with rat sized toys and tunnels. Pringles tubes make good floor tubes!
I think it comes with a litter tray doesn't it? That helps massively. They will use a litter tray if you put it in the right place - ie the place they have chosen as their pee spot. So if they don't use it where you've put it, move it to the place they've chosen - often a corner of the cage.
Chinchilla bathing sand is best for the litter tray - it soaks up the pee. Or some people use childrens play sand from Argos (check it's sterilised).
What else. If you're using pine shavings, check on the bag that they are kiln dried and dust extracted. If you want alternatives at some point, Fitch is very popular - it's sold in bulk so works out quite cheap and hamsters like it as it's soft. It's recycled food grade paper. I get the 10kg bag and it lasts for ages.
It's better than Carefresh and cheaper and has no dust. You can also mix two substrates together for variety.
https://www.fitchfirst.co.uk/fitch-p...-delivery.html
These are the rodipet houses - the two room one is popular and fits well in that cage
https://www.rodipet.co.uk/houses/rod...t-rodents.html
A cheaper option also with a lift off roof is this guinea pig house (no nails and it's way too small for a guinea pig and a good size for a hamster). It fits together like a jigsaw. That does need a bendy bridge over the door as it has an extra large door.
https://www.amazon.co.uk/Ferplast-Gu...AE2678XT04FGB4
Their house is basically a nesting box.
If you get a wood one then you'd need to paint it with plastikote - the enamel paint on version is pet safe and virtually odourless - dries very quickly.
https://www.amazon.co.uk/gp/product/...?ie=UTF8&psc=1
It comes in different colours too if you wanted a colour splash!
Suitable nest/house and moving cages
I’ve realised the pico XL cage that we have is not suitable so have ordered the Savic heaven cage for tomorrow and will take the tubes and penthouse out much to my sons disappointment. My son didn’t like the Alaska cage (is his birthday present so wanted him to pick) and I haven’t got space for anything bigger, to be honest my hubby is already going to get a shock and won’t be happy on the size when he sees it! 
Any tips on what to get, what not to get. At the moment in the old cage I have a wheel, cardboard tube and a wooden tunnel to climb on or hide in, a few wooden chews. To put in the new cage also have a tube seesaw.
Re: Suitable nest/house and moving cages
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