I would not use a jack shaft. Jack shafts are used primarily to align drive chains where mounting is offset, or where chain run is excessive. You are dealing with neither of those issues on this bike.
Restore it as you are planning, and use the standard entry level clutch. Your seven year old isn't so heavy that the clutch will burn up quickly.
Those clutches start to engage at around 2000 RPM. I would not let concerns about burning out a clutch drive my decisions on power train. Instead, build the bike as you intend, no jack shaft, and concentrate on that, with an initial means of limiting RPM, or even sitting behind him as he learns to operate the throttle and brakes. (grin) That last- riding double and putting around, is hard on clutches. Make sure you oil the bushing well, and often, keeping the oil off of the shoes- only on the bushing.
I'll bet he is able to handle the bike pretty quickly.