lol @ patio.
If you can get him 12 hours a night on a schedule (10 bare minimum) that can really mellow them out a bit in terms of hormones and it also is essential for immune function. So, you might want to try gradually getting him to bed earlier if he's waking at 4...or darken his sleep space and put him in a quieter room so that he can sleep past 4.
You didn't mention the huts/tents. Are there any in his cage?
You CAN teach them to play with toys (by introducing them really slowly from many feet away and modeling play/rewarding any interest/proximity to the toy once you get to the point of moving the toy closer), but what you said abt being picky also applies here-- they don't all like the same types of toys. You might try wood, sea-grass or shredding types of toys (based on his paper-towel interest). You do want to be careful with paper-towel rolls due to the adhesive on them. Same with books- the inks/adhesives can be unsafe, so just be aware of that.
To improve your relationship, try to associate yourself with as many low-key/low-stress things as possible and positive things that he likes (without trying to force him to do things if he hesitates) They move in slow motion.
You may want to try cutting back on fruit some, as the sugar can impact them. It's fine to give a little bit daily, but think about how small he is, and think about the fact that a grape to him would be like 100 to you lol.
Does he step up willingly?
Any behavior issues?
I am not criticizing what you are doing-- AT ALL. I am just trying to see if I can help, but if it "aint broke"....