That's a nice looking house for sure. I agree with rebuilding, but without very strong framing from the ground up, the solution is not permanent to any extent. Just about have to use steel framing for that it would seem, but I don't know, just my intuitive opinion.
With the strong framing, which may could be replaced without tearing down the building, the roof will have more support. Any structural movement of a domed roof will cause it to leak. I would say that the cedar shingles (which look good on that house) would work out fine, provided the frame and sealing work was addressed beforehand. Less movement from shifting and settling caused by weather on the roof will mean less leakage. Also with weather extremes, a solid foundation will steady the house from wind effects, which in turn place stress on the roof.
Interesting to note, there is a dome structure here in Mobile that is a tavern near the lower river delta on the causeway. That place has been there for at least 25 years. The design apparently is hurricane resistant, as this structure has weathered several strong hurricanes over the years. The shingles are cedar, and it is built on telephone pole piers about 20' high. It's one of the few structures that is a survivor. Don't know if the roof leaks, but by golly hurricanes don't seem to bother it.
Les