Grant there are 2 schools of thought on flex, 1 use the stiffest flex you can swing to improve on accuracy, 2 use the softest flex you can swing to improve distance.

I don't know the difference in A3 and C3, but since A3 is with a stiffer shaft I would guess it to be loftier.

Now to your question, if I had a pro that knew shafts and heads and what not about fitting, then that is who I would go to and I would not go to someone else afterward, if I went to a fitter first then I wouldn't go to someone else afterward.

It sounds like your pro felt that R is stiff enough to handle any swing flaws you have in your smooth swing, and he would like to keep your smooth swing smooth. With a stiffer shaft you may get unsmooth because it doesn't feel like you are loading the shaft. And the next thing you know you are starting your swing at the top and flipping at the bottom or simply throwing the club OTT.

Update...just played a round with the stiff flex Kai Li, 9.5 head set at C3 (slightly closed slightly upright).  I felt as if I really had to go after the ball more than I normally do.  Distance and were comparable to previous sessions with regular flex, same setting.  I guess I should go hit both back to back with my teaching pro....

I have been face with a similar problem recently. What I did was select the shaft I felt the most confident with. My thinking was neither shaft selection was a bad selection so I the golfer should make the call.   I know and feel your pain.

I would tend to rely on the fitter, but get both people in the room and have each put forth an argument as to why their case is better.  Be the judge and jury!