after stunning the pig with the air cannon,

here are some figures to peruse over the turkey and wine.
As an alternative to automotive servos (car-window, windshield, etc) another,maybe better, idea for the driver would be an electric drill. In fact old electric drills might be more ubiquitous, might have more power. Plus if it is a variable speed drill you maybe have a way of controlling the speed. Occasionally can find old cordless drills at thrift stores, or in your own junk pile. They're probably there because the battery died, with a motor and gears that are still good.
I'm glad you know how to weld, as I was imagining this whole thing made out of steel.
Regarding the question of how fast it should go, recall that power is torque times angular speed. P = τ * ω Convert the English units to metric first. Convert ft*lb to N*m and convert RPM to rad/s
1* ft*lb = 0.3048 m * 4.4545 N = 1.358 N*m
1 rev/minute = 2*pi/60s = (pi/30) rad/s = 0.1047 rad/s
The product of N*m and rad/s is power in Watts.
For the hypothetical example of 60 ft*lb * 1 RPM get
60 * 1 * 1.358 * 0.1047 = 8.5 W
And I think ~10 W is a good ballpark estimate of how much power you can get from your drill motor. So I think my earlier guestimate of 1 RPM for the angular speed of the spit is still a good goal to work towards.
I imagine gearing down the output from the drill with bicycle gears, and I have drawn a crude picture of this. I drew two gear sets, but you might be able to get away with one... or three... dunno that's for you to figure out.
gears.png