Yes, the crankshaft confers the greatest mechanical advantage at the top and bottom of the stroke; that's an excellent observation. The position vs time plot of a crankshaft follows a sine wave, the velocity (as a derivative of position) follows a cosine, and the acceleration available from a constant input torque follows the derivative of the position, again a sine wave. However, this available force does not meant that the exerted force at the top of the stroke is high, as it needs a reactive force to work against. This force is mostly provided by the fluid pressure, rather than by a velocity-dependent force like friction.

At the top of stroke, the gas is not under significant compression, so it takes minimal force to move the piston. Near the bottom of the stroke, when the gas is maximally compressed, there is maximum force on the piston. When the pressure exceeds the output of the compressor, the air begins to exit through the check valve. Another complicating factor is that there are typically two pistons on the same crankshaft, so as the piston returns the gas remaining in the cylinder is working with the motor. The final and most complicated part of the problem is that the whole point is that the gas being compressed is not an ideal Hooke's law spring where PV = constant, it's undergoing adibatic compression, where P x V x gamma = constant, where gamma is the specific heat of the refrigerant, and the temperature changes through the compression.

You can improve your intuitive understanding of these relationships with an ordinary bike pump and the bike's pedals. When the pump is fully up, there's little resistance, you can feel the force increase when it's almost at the bottom, and you can feel and hear the air going into the tire for a short length of the stroke at the bottom. Likewise, pushing vertically on the pedals (avoid pushing forward or pawing backwards) does the same thing as a crankshaft.