Tim,
You are correct about the cycle time, however, the thermostat (If it's a newer electronic model) should have a built in time delay to counter this.
A solid state adjustable time delay=(Delay on make) Johnstone Supply ICM Controls, 3 minutes fixed, #B11-832, $9.21 is available, simple hook up, just 'break' the red, or voltage wire in the thermostat circuit, one wire in, one out of the 2"x2" delay module. I carry 5 or 6 and install them on units I service.
Tim, I am puzzled about the change in fan speed, causing problems, sounds like there is a conflict in voltage-amperage draw there. I would take the fan power over on it's breaker, and move it to another breaker, or give it it's own, to see if that solves the problem.
I think 315RLS stated he had a fan motor hang up.
Ozz
'07 3400RL 2nd RTU
2 Golf Cart batteries 1500 watt inverter
Honda 2000 Generator, 2nd one and twinning kit coming
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Stationary domed Sat. dish
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3 added 120 volt outlets
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2006 Ford PSD 4x4 Off Road Lariat
Hadley Air Horns
Truck inverter with 110 volts for laptop
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Awning lock