I can understand your feeling clumsy when shifting. I don't have an answer for you but do remember when I had to do that fifteen years ago with my old Nishiki bike. Hope someone supplies you with an answer.
Practice, practice, practice is the key. Will you ever really feel stable and quick when you have to move your hands from the bars to shift? Probably not, whey else would they make such a big change to integrated shifters. Not sure what to tell you that would really help.
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