Should be easy to discern headset looseness from brake death shudder. What's the frequency of the back/forth oscillation? If it's about once per wheel rotation, it's headset (Also, if you can apply the front brake fully when stopped, push back and forth on the bars, and feel a knocking sensation, it's the headset). However, if the frequency is a lot higher, and feels like a resonance effect, then it's death shudder.

Death shudder isn't all that well understood, and preventing it is generally a matter of trial and error. My bike does it with the new brakes I bought (good brakes, too). It just happens with certain combinations of frame/fork/brakes.

In order, I would try these:

*CHECK QR TENSION (!!!)
*change toe in/out.
*change pad angle on the "roll" axis (if that makes sense).
*tighten brake pad retention bolts
*tighten brake arms into the cantilever bosses - you might need to add a washer or replace the bolt if it's too long
*Clean rims and pads
*Alter headset tension a bit (even if it's not technically loose - just don't make it too loose or too tight)
*Sand the pads to get rid of glaze (usually temporary relief)
*Replace brake pads with different type (kool-stop salmons, in particular)
*Change brake arms to something lower-profile that might not bend as much.