Using Surface features is probably your best option for this.
Can you attach your part?
One way to try it - see attached
But I bet that Paul Salvador would have a much better answer
Here is (edit and clean)
I did try to do this with the dome feature and got a great preview but it failed.
Spot on my friend,
This is why I mentioned using Surfacing features above because all of the pre-requisites where there.
Of course,,, you were my inspiration Dave.
It's obvious that Jordan would like to use the sketches to define dome shape but, of course, you cannot extrude up to them but you can a surface. I also did this with the boundary surface and a boss then replaced the face.
Easy peasy. Start a sketch on the face of the base, convert the face profile with a line cutting it in half then revolve it.
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