Actually Tabby, those are absolutely wonderful suggestions. You are one rabbit savvy amateur!
It is so true about schedules - It can make them feel more secure. Being prey animals, knowing what is coming next is calming. I know this, but always forget to use that and I think this advice can also help with shy bunnies.
I also think your idea about a second bunny is a great suggestion as well. I do agree that this can really help sometimes. I know my Jack used to really want to tear up the place, and though he is good, and follows orders, his state of being really calmed down once he was bonded with Rucy.
Fujoe, if you do decide to go the route of a second bunny, I really suggest taking Fujoe bunny dating at the your local House Rabbit Society there in Chicago. Let them know what kind of bunny he is (most likely dominant) so they can help make the right match - maybe with a passive bunny, or ya never know - a bunny can really change around another bunny. Fujoe might end up being passive with another bunny.
You will have to go through a bonding period, but if let him choose a bunny, it's usually much less time and stress involved.
My first bunny went through about six speed dates at my local HRS before he settled on one that I would have never picked out. But I love her too bits now.