well bob putting in 'fictional' numbers to get the result you're aiming for is cheating.. and cheating is wrong
Nevermind!
I can (almost) fix that for you with real numbers...
A series 500 TC has a nice wide range of gear reduction..
low end 3.34:1 and 19% overdrive (0.81:1 high end)
gives us a total of 3.53
50 / 3600 *1600 / 3.53 = ~ 6.3
6.3 mph doesn't sound too bad and the industrial engine is back in the game, no?
and a minor governor adjustment (say 4k rpm)
in case the manual allows for such like the honda would,
could get that even down to 5.67 mph

the series 500 can even engage at lower speeds (850 rpm is the lowest engagement speed)
But that depends on idle speed of the engine of course, since we don't want the TC to engage prematurely
I still wonder about the drum and all that...
I mean @ 50 mph we talk about .833 miles of cable every minute
and a minute of fun isn't that long either, is it?
So however narrow that spool would be, it would grow in just a few seconds and thus bring the speed back down considerably, no?
(assuming it's not 30 ft wide that is

)
So you'd need a wrapper spool (pulling the cable in at the intended speed)
holding say five to ten wraps of cable only just to get the friction covered
and a collector spool behind that (running at a different speed to spool up the miles of cable)
The latter doesn't need that much power I guess,
so splitting the output of a single engine to power both at different speeds could work,
but the setup will be rather complex I imagine,
especially since the collector had to run at a variable speed whereas the driving spool should run at a fixed speed.
series 500 driven powering two sprockets on the other end of the jackshaft is the easy part,
but getting one of those to go slower when needed without affecting the other... IDK *shrugs*
'sid