beak wrote:

 I'm beginning to wonder if such ball-bearing slides are not intended to be oiled at all -  they appear to be well oiled at present..

I have had some success with lithium grease (not oil) on ball bearings. It stays in place longer than oil. Worth a try. I greased the bearings on my Hermes basket-shift mechanism. They were also held between rails. I just put some grease in where I could reach smeared it around with a toothpick, shifted a couple of times and then wiped away excess. But mine weren't already oiled...

I used it on a hunch, not based on any research. If I run into problems, I'll post them here so others can avoid.

Update.
Today compared problem SG1 shift with two working examples - no difference in feel whatever.
Feet are not the problem.
Drenched all shift linkages and the ball-bearing section with degreaser while operating the shift scores of times, and re-examined all linkages for distorted parts and for any possible rubbing contact with any other parts - nothing.
No change at all, and I'm completely stumped!

I checked the springs - they are sound and tight, and I wound the assist adjustment up to full anyway.  I don't think this is the problem because once that first half-millimetre of travel is caused by hand, the basket raises strongly and normally.   By the feel of it, there is certainly something fouling or sticking somewhere which simply prevents the action from beginning, but once started, it is normal.

I promised to keep my nose out of this sub-forum, but...

Have you checked the keybar comb under the keyboard? If the teeth of the comb are not perfectly parallel they can cause the shift key lever to bind, even just enough to jam the action.