Just a little random update:
I've been using my bike a bit more recently. Consequently, I've been loading and unloading the tree more frequently. It is functioning nicely and is plenty sturdy.
My only complaint is that I didn't buy bigger hooks for the bike tires to rest in. My 26x1.90" tire fits well, but the other bike's fully-inflated 26x2.1" tire takes a bit more conscious effort to hook on.
Nonetheless, I still consider this project a success!