I'm pretty sure indexing doesn't really deteriorate as STIs age; they were designed well in that respect at least. Your levers are prolly fine.

However, your RD has some serious miles on it, and the issue you describe could easily be attributable to a worn one. Fresh pulleys won't do much for it either, since wear at the upper and lower pivots, and the parallelogram pivots, all adds up too and can't really be fixed. Check for RD wear by wiggling the bottom of the cage from side to side and looking/feeling for slop at the various pivots. Compare that amount of slop to what you can feel on a new bike for some perspective.

It's almost certainly worth grabbing yourself a new RD; Shimano ones weren't designed to be all that durable (recent ones look better, with wider parallelogram arms) compared to Campy. If you do that before putting on a new cassette and chain, you'll isolate the issue. I'm tipping you'll see an instant improvement.

Still, I might be wrong, and it might actually be shifter wear. If you think that's the case, maybe you can borrow a newish RD to diagnose it before you start buying parts.