Thanks for all the advise - maybe he doesn't love climbing like I thought. I feel like a bad mom! But I will make things right. Pictures to follow.
Think I decided I'll create the bin cage, if I find a practical way of attaching the other cage great - if not no worries. Additionally if long term the wire cage still seems like bad idea or it's not used by him anymore I can seal the connecting hole up with more mesh so no real harm, done!