I think I see the pulley issue now Dave: a split V-belt pulley (split at right angles to the axle), and you change its effective diameter by adding or subtracting shims between the two halves. Traditional industrial sewing machines for shoe-making used the same system, with a pedal to vary the pulley width - that was the way the operator adjusted the sewing speed. Those sewing machine pulleys can be a cheap way to get an odd-sized pulley for projects. I have one of them on my disk sander, since I replaced a burned out 1500 rpm motor with a 750 rpm one (I got a good price on the motor) and needed to get the spindle speed back to the required 2,300 rpm, accurately.
I don't think your Imperial would have a split pulley to adjust belt tension, since it has a movable idler to do that. I think its purpose would be to adjust the forward self-propelled speed of the mower over the ground: the split pulley is on the output side of the reel, which drives the rear roller. So, you would change the shim stack in the split pulley until you found the mowing speed to be comfortable and effective. Adjusting the split pulley does not change the reel speed, only the roller speed. Thank you for showing us that - I previously had no idea the Imperial had a way of adjusting the roller speed.
So far as the take-up speed of the centrifugal clutch is concerned, it is rather a difficult point. The Briggs engine is supposed to idle at 1,750 rpm, so the centrifugal clutch should engage at a speed between 1,750 and 2,000 rpm. You would need to use a tachometer to check what it actually does. Unfortunately the mechanism in the clutch always has some friction so engagement speed tends to vary just slightly even if the clutch is in good order. It would be useful for you to do some tests and tell us the measured engagement speeds - we can then discuss whether it is suitable or perhaps the clutch needs servicing.
