To the OP: I had exactly the same problem with my Radial before sending it to Anderson Plating for overhaul. Tried everything with the valve like you did, problem was still there intermittently. Told Anderson about it, they could not replicate the problem. Upon receiving the horn back from them, problem was still there, driving me nuts. I found out accidentally that it was actually the slide rattling, not any part of the valve assembly.
I'm not sure what has been said throughout this entire thread, but it might actually be your 2nd valve slide that's a little loose and produces the noise. To find out, push against the slide with your palm while playing a note with the 2nd valve pressed. If it makes the springy sound go away, that's it. Then, try taking the slide out, apply a generous coating of thick grease (I like the Courtois for tuning slides or slides that don't move), put the slide back in place and push it firmly in to make sure it's in all the way, and see what happens. It's worth a try at this point.