The contractors may or may not be idiots. If they did a manual J to correctly size the unit it could be designed for both units to be running and for them to both be on all the time. Manual J is the industry standard for sizing. Ideally an A/C will run 24/7 when its at design temp outside. Thats when its most efficient starting and stopping all day wastes energy. Your unit is grossly over sized(i.e. inefficient) going from 85 to 70 in an hour. This could also be why you have to have it so cold because an over sized A/C doesn't run long enough to remove humidity. You sound like one of those idiots I encounter all the time that set the heat to 80 in the winter and the a/c to 65 in the summer. Mine stays at 77 in the summer feels great and costs me almost nothing every month.
I completely trust the contractor that sized and installed our unit, and I don't know anyone whose A/C unit runs constantly to keep the house at the desired temperature. I've never experienced an installation, in 40 years, residential or commercial, where the unit was sized to operate 24x7 in order to maintain temperature. Beyond that, no, we don't set the temperature to 80 in the winter and 65 in the summer. It's 74-76 year-round.
Edit: really, 68-76 year-round. We tend to set it 68-72 in the winter, and 74-76 in the summer.
Edit2: information on the manual J method of calculating heat load that I can find indicates the goal is to have the system sized so that it operates continuously at 110 deg. F. The cooler it is below 110 deg. F. the more the system should cycle. Based on that, and the operation of our own system, I would say it is properly sized. We don't have a humidity problem. It's also even clearer, having read the information on the calculation, that the OP's system is not functioning correctly. Given the advice he has received from the contractors I stand by my original assessment, and that's about all I have to offer on this thread.
"There is no exact answer for how long your system should run during
each cycle. The average air conditioner is sized to remove the heat
from your home as fast as it comes in, on a 110° day. Therefore,
ideally, on a 110° day the system should be able to keep up with
the incoming heat, but not gain on it and be able to turn off. The
cooler it is below 110°, the more the system will cycle on and
off."
http://www.chasroberts.com/knowledge-center/faqs/#6