C177 pilot reported engine abnormalities during cruise resulting in a diversion. The engine completely failed right before touchdown.

Narrative

Pre-flight revealed no abnormalities with the aircraft. I could feel fuel in both tanks with my fingers and the totalizer had calculated that there was about 35 gallons onboard. The oil dipstick showed approximately 1/8th inch below 6 quarts. During engine run up each magneto showed a drop of about 100 RPM; and the prop cycle was normal. All temperatures and pressures were nominal during engine run up and subsequent take off. Winds were light; out of the south so I took off runway XX and made a left downwind departure to the north. During take off full power was set; roughly 27 inches of manifold pressure and rpm was right at redline. As soon as the runway lights were under the nose I retracted the landing gear. At about 1600' I turned left and retracted the flaps. In the downwind I set climb power of 25/25. Climbing through roughly 3000' I contacted Center for VFR flight following. Shortly after I leveled off at 5500' and had the airplane trimmed out. A few minutes later I smelled a sweet oil smell in the cockpit and immediately looked at the JPI engine monitor and began to watch the oil pressure drop. It was initially above 40 PSI; which is low as the airplane typically would make 65 PSI of oil pressure. I watched as the pressure continued to drop at an alarming rate. At this point I advised center. I looked at the sectional moving map I had on my cell phone that was in the yoke mount and saw ZZZ1 [airport] ahead of me; knowing I could not make that airport I remembered that ZZZ would be close by. I then put XXX.X into the com 2 radio and began clicking the PTT for lights. It was around this time that the oil pressure dropped all of the way to zero and the propeller governor lost control. The RPMs then rose to between 2800 and 2900 RPM. At this point I began a left turn towards the lit runway at ZZZ and extended the landing gear. Airspeed had decreased to roughly 120 mph and the propeller had come back to a nominal RPM of about 2200 rpm. Manifold pressure was moving between 9-11' however I do not recall what adjustments I was making to the throttle at this time. As I continued the turn to a short final at ZZZ I extended 20 degrees of flap and began an aggressive slip to dissipate energy. At this point ATC was reading all of the NOTAMs which was an unwelcome distraction and he also asked if I could copy a phone number. As I began rounding out airspeed was between 80 and 90 mph and I turned off the magnetos; moved the mixture to idle cut off and closed the fuel valve. At this time I called for doors to be unlatched and cracked. The propeller then went from windmilling to an abrupt stop; compared to normal engine shut down. During roll out I was aggressive on braking and the aircraft skidded to a stop midway down the runway. At this time I called for evacuation; leaving the master switch on so there was light on the runway. After it was obvious there was no fire; I reentered the cabin and attempted to contact center from the ground and then made a call that we were down and safe. I contacted ATC via cell phone and let them know the aircraft was still on the runway. The airport manager arrived shortly after and we moved the aircraft off of the runway.