I`m in New Zealand, I too have a cottontail house bunny. Here I`m not allowed to release bugzee back into the wild. Here they are classed as a pest! (Thats any bunny that has been released or cotton tail breed)
I do have another rescue bunny called Shadow. At the bottom of this message is a link to my photos. Could you have a look at Shadow and Bugzee and tell me if you think Shadow is a cotton tail please. Bugzee is 100% cotton tail.
Looking forward to seeing some photos for your darlings.