This 2003 STS had a shimmy. Went through everything under the moon 3 times, $$$$ and it came down to strut mounts. All the crap I went through and it was a $400.00 fix. You may hear a dozen other fixes but it all comes down to what I found.
Don't hang you hat on the same fix for all FWD Northstar vehicles with odd vibrations at odd speeds and odd times. Over the years we have seen everything from bad tires, bad balance, rotors, hubs, pads, sway bar end links, struts, lower control arm bushings, hub/rotor faces with runout - you name it.
The vibration diagnosis chapter in the GM service manuals for these cars is quite large - and covers many diagnostic techniques.
It would be very unusual for a strut mount to cause the issue, not saying couldn't happen mind you but to post this is the only fix ignore everything else is not a good recommendation.
Rare and unusual fixes are hard to track down and many times the solutions are a combination of things.
Yes ima dig up an old thread, but im experiencing the same thing on my eldo, and have new-ish strut mounts.I might be due for new rotors and pads and yes i know my rotors aren't warped. so i might need ball joints tie rods, etc inspected.