Hi Katie and congrats on becoming a bun mom! My bunny Toki is a not a lionhead but I thought I would add my two cents just in case you can glean anything relevant or helpful from it. From what I do know about lionheads, their fur can become matted if not groomed regularly. Also as with all bunnies, they need regular grooming to remove loose fur that they may otherwise ingest. For the de-matting, I would suggest trying different grooming tools. For Toki I sometimes use a grooming ‘glove’ since he also hates brushes with a passion. The only thing is he will try to eat it and attack it if it gets in front of his face. Could something like that help with de-matting your bun? Have you tried a variety of different brushes on Taylor? Some can be quite harsh and aren’t really suitable for a bunny’s sensitive skin.
When it comes to grooming in order to remove loose fur, I would suggest the damp-hand method. There’s a video by Howcast on YouTube called “Do Rabbits Shed? | Pet Rabbits” where that method is demonstrated. Toki personally loves this method because he just thinks he’s being stroked. I put a water bowl on the floor, lightly dampen my hands with it, and run them all over his body. (Obviously make sure bunbun does not get truly wet.) Then I rub my fur-covered hands together and collect the furballs onto a paper towel. It’s not painful or harsh for him, and he would happily let me do it every day. When Toki is shedding or moulting, I will simply pluck the loose excess fur (as is also shown in the video I mentioned), in addition to the damp hand method, multiple times a day depending on the need.
Not sure if any of that helps or is relevant. But I hope you find a method that works for both of you and helps you enjoy a close bond with Taylor. 