I saw this dome and arch detail in an old architectural book, it was easy to make the arch and dome components but I do not have any idea how to bridge the gap between the two shapes, any suggestion would be greatly appreciated.
You can try to use first the function Shape | Other shape | 3-4 curves...Select your 3 boundary edges, then apply...Check the olh to learn more about the options of this feature...
I downloaded your files, and the solution was not really the 3-4 curves...I copy the boundary edges, trim the circle edge, and create a Constrained surface, as you can see in the linked file...Just have a look in the design tree, to understand how I made your fill surface...
Thanks for taking the time to take a look at the file and coming up with a solution, i'm going through the design tree trying to understand what you have done, those are new tools i have not used yet.