The kit is still available.
And like Norm, I never remember that link is down there!
It is Not linear.
And it is Not bang-bang.
I like to think of it as PWM with a self adjusting frequency.
4 parallel fets will handle 1 ohm fine. I think 3 would do it fine, but with a homemade resistor, 4 is probably a good idea.
I suggest each Gate have a balancing resistor to keep the fets switching more in time with each other.
I suggest the fets all be from the same production lot (from the same factory packaged tube).
The frequency was intentionally slowed down to keep the yellow LED on longer,
because if people could not see the Yellow LED blinking, they thought the circuit was not working.
The pics below show it with a lower value cap than is in the kit.
Medium duty cycle, with a medium charging current.
Higher duty cycle, with a higher charging current.
"with a much sharper transition than directly zener -> gate driven response would be"
Not a good idea.
A Zener driven fet Gate would have nothing sharp about it.
I kind of doubt the battery voltage could be controlled within a volt, and maybe not within 2V.
That type of thing would be better off using some big TO-3 bipolars, if you can find something suitable that costs less than a...?
G-