One serious problem with the selector mechanism in the 3 speed Bantam gearbox is the huge amount of lost motion within the mechanism during actual gear changing. The same applies to the 4 speed 175 unit but nowhere near to the same extent. Lost motion always leads to a long change lever movement, precisely the problem you are describing. I well remember changing gear on my work hack D14/4 by having to lift my foot clear of the foot rest to effect a positive change.
From a purely engineering standpoint what is required is to convert rotary motion, to linear motion then back to rotary motion and simultaneously provide enough mechanical advantage to overcome basic friction and spring resistance. Easy to recite but tricky to implement!
The device in your post when attached to a Bantam situation would work but looks complicated, and has lot of connecting points to create slop and lost motion but how large would the whole thing have to be? I tend to try and keep things simple, a conventional linkage such as on a RS Honda would do the do the job very well particularly with rose joints and robust adjustable linkage rods. You could measure up the system on Derek`s RS? A bespoke set up could be drawn out on paper and the various levers adjusted to provide the appropriate foot change motion that you want and corresponding movement in the gearbox. However, short levers (small mechanical advantage) require a larger input of force to achieve the same as a system with long levers, and it is a short lever motion you want for the foot change.
I don`t think I have been of much help but Bantams seem present a problem in almost every respect!