I should have mentioned that the bike I had that shimmied before I moved the rear rack forward a bit (about 1/2 inch at most) was a steel BIANCHI MTB with straight bars. I later converted it to a dropbar.
I think that at the time of shimmy it was with a Blackburn rear rack but I'm not positive.
I did not have any problems with that bike when I toured on dirt logging/mining roads and was using Nagaoka front and rear racks. I loved those racks and would love to get another pair. One of the things I liked about them were that both had semi-lowrider attachments on them. One the rear that meant I could carry something on top of my side-opening panniers.
Here are two poor images* of that BIANCHI MTB with the NAGAOKA racks whilst I was on a two-weeks long unsupported tour of logging/mining roads in Northerm Ontario, Canada back in the mid-1980s.
If anyone knows where I can get a pair of those Nagaoka racks I'd really appreciated hearing about it. VBG
Cheers
* Images are scans from 3" x 5" photos.