Hi!
If you look in the cage reviews on this forum there are lots of big cages, but honestly, i'd try eBay first, I get all my cages from eBay, as I simply dont have the funds to pay high street prices!
A zoozone is a large spacious cage, and often appear on eBay for less than £30, even new. I think seapets sell them too at around £40 new.
If you see the reviews for this cage, it is a flat level cage so you may have to be a bit inventive, and as it is sold as a dwarf rabbit cage, you'd have to mesh the top to prevent an escapee!
Hamster heavens are absolutely massive-and i have seen them on eBay, one sold for about £16 recently, another cage to look out for.
With regards to the house situation, i wouldnt worry too much, neither of my syrians sleep in a house, despite them having large igloos. Just make sure he has plenty of bedding
Not sure what to suggest with the wheel-although i do hear Wodent wheels are quite good, you can get them online.
With the ball situation, might be worth you investing in a play box/pen of some sort with some toys in it for him to play with so he can free range run instead. The runner balls seem to come in standard sizes, but of course, i could be wrong and someone might be able to suggest a ball for the more portly hammy?
Only thing with play pens is, you have to watch them at all times. Syrians can be up and over it in no time, but do tend to give up trying to get out if you keep stopping them, and go off and play
250g! That is huuuge! I'm curious how mcuh mine weigh now, i might have to plop them on the scales tonight and see
Good luck!