How can I get the compressor to cool the A-coil for 30 seconds before the blower engages?
So you want to shorten the life of the outside unit, why? Relay's are used to usually keep the outdoor unit from coming on right away, if there is a power drop while it is operating, and power comes immediately on.
As long as the outdoor unit and indoor coil are doing their job, and the inside air handler/furnace is also doing its job, there is no need for a 30 second cool down. Matter of fact, with my a/c, I can stick a six pack of beer in the vent, and cool it down within a hour of running, due to always pushing at least 36 degrees, no matter how warm the house is during the Summer.