I've got to disagree with you Charles...
Yes indeed there was a 1966 Lady Kenmore-esque 900 washer with a Vari-Flex, oddly enough I just came across a parts list for one yesterday when I was organizing paperwork that I didn't even know I had.
A couple years ago James and I did a lot of research on the long lineage of the 1966 Lady K and the many "side models" or shall we say "cousin" or "sister" models that were spawned from it. This was sparked in part by the Avocado 66-like set that I have that are 900s but not Lady Ks.
What we found was that there are four 1966 numbered models in the 900 lineup that all look identical to the Lady K, save for the Lady K name plate vs. the Kenmore 900 plate that the other three received. I will give you a little summary of them:
Model 110.6604900 - This is the real and original 1966 Lady K
Model 110.6604910 - This is the first sub-model, and is the one I have. It has a two speed motor instead of the LK's 3-speed. It says "Kenmore 900" on the name tag.
Model 110.6604920 - This is the version of the 900 with the Vari-Flex
Model 110.6604930 - This model actually uses a Roto-Swirl. I was surprised to find that one!
Note that the final digit in each number above ends in my example in zero (0). Numbers higher than zero here are simple engineering revisions to something in the machine that does not affect its features. Often a change in timer part number will result in an engineering revision of the model, as well as other changes, but the basic machine stays the same.
These sub-models were created to allow Sears to nearly always have some sort of high-end washer on sale, so they could advertise accordingly. One week model 26900 would be on sale, next week model 26910 would be on sale, and this way they get around retail law that would otherwise require the list price to be lowered if the model was almost always on sale.
Because model 6604920 LOOKS exactly like a '66 Lady doesn't necessarily mean it was out and available in 1966. I say that for three reasons. This being the first version of this model, it should have 1966 features if it was a '66 machine, but looking closely at the parts diagram, you can see it has the later plastic detergent dispenser lid - the color coded one to match the cabinet, with the chromed plastic bezel.
You can also note that the part number of the Vari-Flex agitator is 362010, that is a later part number not yet issued in that range in 1966. For comparison, the part number of the 1968 gold Straight Vane agitator is 360646 (this is the first gold version that replaced the bakelite 6-vane agitator).
Finally, nearly every Kenmore parts list carries a date on it either on the front page or the last page, which indicates when the drawings were created for that model. The 6604920 says 2-69, so Feb. 1969. Parts lists are always created before a model goes into production and sale. That is consistent with the plastic detergent dispenser cover, etc.
I really don't think the Vari-Flex and the so-equipped '66 900 were available in 1966 as it would otherwise appear.
Gordon