Make certain it's the STI and not the cable binding somewhere. I might pull the far end of the cable out of the housing till getting to the one that is under the bar tape. And then put a little tension on the cable as I shift up and down. And if that's no change, I'd remove the cable entirely and try to gauge how much resistance as I remove it through the STI. It's possible you might have a frayed cable in the shifter. Those usually show other issues long before being thought of as a gunked up STI.

I wouldn't flush a STI unless it's a last ditch effort to make it work easily.

Have you clamped anything around your bar that might be collapsing the cable slightly? I did that once.