In the first instance I removed the lower fixing plate and the runners -- but still far too high; and now no fore and aft adjustment -- useful for long legged critters and short granddaughters. So out came the trusty angle grinder for major surgery.
Obviously, one cannot remove the bottom plate entirely as the springs and shock absorber are attached to the lower sides that are welded to it. But it is possible to cut off about three quarters of its length. Having done so I then removed just under two inches of most of the side plates -- again leaving enough meat to support the shaft holding the springs etc. Also room had to be left so that the seat pan's two front support arms rise and fall would not be obstructed, thus defeating the purpose of a sprung seat.
This is the result.

No comments about the weld, please. The initial seam was neat, but I decided to re-inforce it.
Next up was to provide fore and aft movement by drilling two 1/2 inch holes and angle grinding the strip out between them.

This was then offered up and tried out -- and, as the good Book says, it was good!

In the pic above you will notice that there is room to add a length of 1 inch angle iron as added support to the mounting platform. I will add this at a later date as I believe it leaves room to flex with possible disastrous results. Even so, the spinal cord now appreciates the ride.
Pavel