It is possible to read on the internet a lot of parroting of the notion that front derailleurs are basically simple and their compatibility specs are more malleable than that of many other components.
This is a good case in point as to how that is just not true. You are running up against the spec that Shimano calls "Applicable top-mid tooth difference." They've changed the verbiage a little over the years, but the gist is the same. This number cannot be cheated by even one tooth without starting to cause the issues you describe.
In the beginning of Shimano road triple from the late 90s, they were doing 30-42-52 as standard, and the FDs of that era had 10t for this spec with total capacity 22. They then moved into the more practical 30-39-50 and it became 11 with total capacity 20. Microshift makes 9-speed STI-compatible repair FDs that have the older 10t, 22t capacity spec, which relates to the cage shape and what it's contoured to work ideally with. You could think about getting one of those and going 26-38-48 on your existing cranks (38t is the smallest possible 130 ring). You could probably make that function, but the catch is that 130/74 ring sets in that combination that are made to play nice together vis-à-vis shift aid/ramp positioning don't really exist. You could probably get it a lot better than what you have though just using reasonably well-matched repair chainrings.
There is a lot to be said for cutting to the chase and getting 104/64 or 110/74 cranks with something like 26-36-48. Shimano makes various nominally "Trekking" type cranks of this sort, but they basically work with road triple FDs and STI. If you do that with the FD you have, you're cheating the total capacity by 2t, and the consequence of that is you will get chain/cage drag on some small/small crossgears, which is not a big deal for most on-road use since those are unimportant gears. With STI, it cannot be understated how much better the shifting performance is when it's a matched ring set like you get on a crank of this sort, compared to putting something together from parts. With other kinds of shifters that matters less.
It's very common for FDs that have gone through a lot of chain drop due to borderline non-functional setups to be in poor shape. If that is true for yours you might consider replacing it up front when making the above changes just to be done with the frustration.