I agree the short cycles are hard on the compressor and needs rectifying.
I'm afraid the time delay will not be completly satisfactory although an improvement. Make sure the fresh air intake is complwtly closed. Otherwise when the compressor cycles off the air passing over the sensor rises and siginals compressor on.
I like the idea of a divorced t-stat. Some but not all pack unit t-stats have a screw for factory adjustment of differential. I would not ordinarily suggest messing with the screw but you sound like you know better than get yourself in trouble. Also,it sounds like the t-stat is probably bad anyway. While looking for the adj screw,get all the mfg info and #s off the t-stat and see if a wholesale hvac supply house will give you a price to order a replacement. I take it from some terms that you used that you are in/have been in the business,otherwise you might get someone who is to order it. If the price is unreasonable,you still have the divorced option.