So here is a potential starting point (to be clear this is NOT ready-for-primetime!) if pursuing the modular approach using modular relays. This would be a compromise between the discrete electronic component approach and a programmable microcontroller (Arduino, Basic Stamp, etc.).
In addition to the 2 relays modules from before, this used a generic basic 12V relay module and 1 garden variety 5-cent diode.
And here it is in action:
As with the discrete component approach, it is too tedious to explain every signal connection. The idea here is to simply present the eBay relay module approach which in this case does not involve soldering or handling a fistful of tiny electronic components. As before the raw material cost would be under $10 if purchased from eBay/Asia.
Given your self-proclaimed comfort-zone, like the discrete component approach, I do NOT recommend you try this at home either!
But I like your idea of approaching an educational institution. For example, this would make a nice senior project if the student implemented several of the approaches with cost analysis, pros/cons, etc. Or even if students are not allowed to operate soldering irons or touch electrical circuits because of liability or whatever, they ought to be able to simulate one or more methods and provide you with a high degree of confidence that it would work if physically built.
Or, perhaps some clever mechanical engineering student could dream up a non-electrical solution where the foot-pedal is modified with some springs, cams, dashpots, or what have you to generate the 0.2 sec open circuit events when the pedal is pressed and again when released!
