I'm not quite sure how much space you have or money you want to spend on a new cage but even though I know you said you don't have tools or anything you can still put together a diy! I was having the same issues and feeling the same way. I wanted to get or make something bigger but I don't have any tools and didn't really want to buy tools. I also have a Syrian and I just upgraded her to a bookcase I got second hand. It's about the size of the 3 level Ikea billy bookcase (31 1/2x11x41 3/4 inches). Although not super tall you can still add plenty of bedding and I think my hamster is a lot happier. I think with Ikea they give you the tools you need to build the items?? or you can get a bookcase already put together. I think where a lot of the diy comes into is if you want to add plexiglass to the front or if you're building something completely from scratch. I still think it is definitely doable and affordable. What's nice about the Ikea furniture is that you can keep adding extensions so if you want something larger you can definitely add to it. You can definitely check second hand stores if you have any around your area or if you have apps that you can sell/buy stuff to look for furniture. If you get something wooden most people recommend to add aquarium silicone to the edges or even contact paper (although it can be chewed easier than the silicone). I hope you're able to find something that makes him happy!!
also hamster balls are not necessarily safe for a variety of reasons
here is a thread I found:
Xmas tree storage boxes are in at Wilko