Thank you for your question.
First thing that comes to mind is maybe it would be best to use the shed space for things that do not need to be heated and leave it separate, because then you wouldnt have to mess with permits.
A monolithic dome "ecoshell" is a small shed available on monolithicmarketplace.com, but its a kit that is essentially an inflatable bag they spray with concrete to get the dome, and still needs fasteners and foundation. Its also vastly smaller than the shed you've got, 8×10, so doesnt really go far to solving the issue. Maybe contact them also to see if they have some ideas.
Our method could work, the block would be that you'd have to find people to do it and currently no one is trained and we dont travel. We've attached to wooden walls with a curved wall as an interface to the round building. Basically we nailed a board the thickness of the wall we wanted to a stud on the corner of the house, then attached our woodcrete forms to that and poured woodcrete right up against the stud on the house, between house and the round building we built next to the house. There are some pictures on our site. Then the round roof needs to be interfaced in some way with your current roof, and the correct flashing for waterproofing will be a must. Once things are attached you'd need to cut away the existing wall betwen the two buildings, likely at one end or the other of your home. Our woodcrete requires extensive curing time so it needs to be fully cured before the wall is cut away. We are currently in the process of doing this, with a work in progress building connected to the house but the wall to be cut out is still there. You would possibly want to reinforce whatever wall you attached to, with extra framing.
It would be unlikely you'd find a carpenter to do something like this, as its way outside the box, as they say. Plus a significant labor cost would be involved, even if you had a local saw mill cut the lumber like we do in thin strips and cutting out the blocks for the roof, the shingles, etc.. We havent done something like that but a mid range estimate might be 35k if we were doing that for a customer. Who knows what a miraculously open minded builder would charge for something similar. Currently we arent really connected with other round builders, but it would be worth it to contact others even if they're not in your area to see if they know of people who are in your area. If you've got any interested adult people around, it would probably be cheaper to send them to a 5 quarter trade school and then have them come back and do it for ya to save labor costs.
Regarding health stuff. Please disregard any of this if its outside your worldview, simply my shotgun approach I share with everyone who mentions health. Wanted to make sure you were aware of doctoryourself.com, a great source for diy megavitamin therapy including high doses of vitamin c; fasting with Dr Jason Fung, a Canadian kidney specialist curing people's insulin resistance with intermittent and continuous fasting; Earthing.com, source for electromagnetic grounding info, anti-inflamatory practice; and ketogenic diet, specifically the book Primal Body Primal Mind, all about the importance of dietary fat from animals and the risks associated with sugar. Also Psych-K, brain hemisphere synchronization, similar to the effect of prayer or meditation. I mention these whenever anyone brings up health stuff. I totally get it if any of that might be outside of your worldview, but if any of that happens to be useful I wanted to share, as health is my other main interest.
Thank you again for your message.