I think it's a great idea to get them bonded and of course it will cut down on the work for you
My thoughts on alternative accommodation for them. If you use your shed, what will you use for your gardening equipment, which is presumably why you got the shed? I think you would also need to get an attached run, so that they could be outside and be secure some of the time. I think having bunnies free-ranging in the garden, whether accessed from the shed or from the utility room, is something I would only feel safe doing if I was outside with them all the time. I don't think it's enough just to be in the house, especially if you are busy with Ted.
Tbh I think by far the best suggestion is to keep them where they are and involve Ted, sitting him in a bouncer. It would keep him amused, keep him away from touching the bunnies or their litter tray and be an inclusive family thing. I would also give you your time with the bunnies without having to worry about Ted. You could read to Ted or, as Graciee said, play music etc. I think it could work extremely well. You could always re-assess when he's crawling, but tbh with a crawling baby the whole house has potential for danger. You just need to be mindful of the things which are super dangerous.
I think you are also possibly over-estimating the work involved with looking after the bunnies. Rugs surely don't have to be washed daily. If they do, then I wouldn't use them :lol: