Sounds like the shifter isn't pulling enough cable. Early on in Shimano's progression to STI shifters the front ders had two different cable anchoring specs. The friction DT levers would use the common cable routing over the anchor bolt. But when STI levers were installed the same ft der needed the cable routed UNDER the anchor bolt to have enough cage travel.

I don't remember all the model numbers that needed this mod but it could be your set up is such a combo. Also your STI levers are old enough so that their internal functions might be starting to fail in that the factory lube can be getting gummy. This stickiness causes the ratchets to not engage and only some of no cable pull will be kept when the lever is released.

I don't think this second possibility is going on but... Andy.