Yeah, I hear what you're talking about!
I might try running it through an amp sim, and see what happens. Even if you want a clean tone, maybe an amp sim will take that attack down a bit. A distorted tone would proabably mask it better, but might not work for the song.
A transient designer plug like you tried would be my second approach, but you'd really have to play with it, I think.
Re-recording the track is not possible? Maybe without the delay?