I agree that the check valve might not be closing fast enough or the inlet of the tank is clogged not allowing the tank to be filled consistently.I think the problem is with the tank. The pressure might be building high enough where it is clogged to cause the switch to shut down the pump and then it slowly fills the tank.The pump will cycle back and forth until the tank is full. I have seen it in the past and its pretty common if you have galvanized fittings on your tank setup or a high amount of iron in the water.
I am not sure if I follow everything but if it happens again I will take apart the check valve and check the tank fill pipe for clogging. We do have high iron around here and the pipes going into the tank are galvanized.
Right now I am going to leave well enough alone until I have more time on my hands to disassemble everything and clean it all or replace the check valve.
Thanks to everyone for the good advice,