Damn oil leak, Rear main??

Clean up the rear of the block. With the trans out you could also grab an oil priming tool and have someone spin the oil Pump to get oil pressure, pull the spark plugs and rotate the engine to get oil everywhere to see if you can pinpoint the leak. Or maybe even just fire the engine up for a short bit of time...Try it a couple times as it seems like you said the problem shows up when you shut the car off. You may also want to make sure the car/engine is level (or as level as it normally sits when the problem occurs). Good luck.