Glad it's a pretty straightforward installation.
I've setup Tiagra triple fd a few times and following instructions it has been fine with brifters.
I suspect the Sora FD for triples is very similar, and one you could find easily (if yours really is finicky)

re your stock bars, one thing to notice with both them and the Nitto ones you showed, is how the drops have your hands (on the drops) kind of in line with the stem clamp on part of the tops.
My Cowbells, and I suspect other similar bars, put this drop area back more towards the rider, which I find more comfortable. Also, my bars are at about seat height, so these two things really make the drops so much more useable than other drops I've ridden.

I see that the Cowbell 3 bars have a slightly shallower drop and shorter reach also than the Nittos.
You can compare these dimensions with lots of other similar bars available now, and also keep in mind the "hands on drops" position -- I totally get what you mean about the curve of the drops on your bars, its something I really like about more horizontal real estate shaped drop bars like mine or the Nittos, but really do like the closer position of mine relative to the clamp on area of the tops.
Hope that makes sense.