To each their own beliefs but for my nickle I suggest priming the engine
oil system with a drill. It has been 5 or more months without running the engine and possibly without
oil in the engine (not sure when the system was opened/drained from the cooler damage).
I also live in the Phx. valley and my
oil temps do require the use of a cooler on my engines so I recommend you put it back on your 392 engine. Do you remember what temps you were running with the cooler installed ?