I think your approach of making the bottom in one sweep, possibly one piece right through if you have the timber (for strength) and the top as a capping is the best approach.
If you shape the capping as a rectangular section (straight and curved) you can use a router with bearing guided bits to get your profile. I would channel out the underside of the capping so it cloaked the joint with the bottom and use a gap-fill adhesive to plant it.
Well I tried to avoid this job but surprisingly they couldn't find anyone else to do it, I had a job cancelled this week so thought I might as well give the handrail a go.
As it was only short I thought it was easier to make it in one piece.
Mainly done with the router but a bit of spindle moulder work and I even actually have to hunt down my spoke shave at one point
I am never keen on jobs like this because one slip with the router or a bit of breakout and it's ruined. There was a lot of climb cuts going on with the router because of grain directions (which I obviously don't recommend).