A Grumman Lynx pilot reported on initial climb after maintenance was done on the aircraft the engine began running rough and oil leaked from the engine obscuring the pilot's view.

Narrative

I brought my Grumman AA-1C to [the Maintenance Facility]; located on the field at ZZZ; to receive maintenance for an upcoming AD that was due. In addition; I requested that they investigate a minor noise associated with the ailerons coming from inside the aircraft; lubricate the canopy sliding mechanisms; lubricate the carb heat control; and change the oil / filter. Yesterday; they called to inform me that the work on the aircraft had been completed and it was ready for pickup. I advised him I would be by to pick it up mid to late morning the next day; which was agreeable.Today my partner dropped me off at the Facility to pick up the aircraft. They met me on arrival; and he and I discussed the inspection for the AD; which it passed; and other minor fixes conducted. They returned the airplane to me in what appeared to be a good visual condition; and noted that they had ground-run the airplane for 10 minutes after completing the work. After settling up on the invoice for the work; I conducted a pre-flight inspection on the airplane as I would prior to any other flight. All items appeared as normal; with the exception of the fitment of the engine cowling; which was improperly latched on the passenger side of the aircraft. I unlatched and re-latched the cowling; ensuring that the inner lip of the cowling was seated inside that of the lower piece; thus being properly seated.Upon completion of the pre-flight checklist; I started the aircraft and retrieved the weather as I taxied towards another Facility; just off of taxiway 1 on the southern part of the airfield. At this time; all engine instrumentation was indicating as normal; I had retrieved weather information from ATIS and received taxi instructions over to the hold short line for XXR on taxiway 2. I switched to Tower frequency and conducted the run-up; which was with no abnormalities observed. Satisfied with the run-up; I advised Tower I was ready for departure; and was cleared for takeoff on Runway XXR with right turnout approved and instruction to remain clear of the Class Bravo airspace (ZZZ1) above. I took off at approximately XA:27am with the intention of an initial departure north and then NW on course towards ZZZ2. This is a short flight; and I would be able to assess that the repairs were successful; fuel the airplane; and return to my home airport at ZZZ3.Engine instruments were reading as normal; and on departure and right turnout; I opted to stay below 2100 ft. MSL until certain I was clear of the Class Bravo shelf of 2100 ft. in the area to the West. I did not change off frequencies after leaving the Class Delta airspace and continued on a NNW departure with a slight climb to 2500 ft. knowing the airspace above and ahead would be 3000 ft. for the Class Bravo. I was 10NM and NNW from ZZZ when the first signs of an issue appeared. In the matter of seconds; the windshield became quickly and completely obscured. Given the atmospheric conditions and outside temperature at the time; I very quickly ruled out icing as a possibility. I stuck my hand up and out of the aircraft to sample the surface of my windshield; and immediately determined it was engine oil. Oil pressure at this time was normal and there were no other abnormal indications on my JPI 830 or other gauges.Over the next 30 seconds; I made two successive 90 degree turns back on course towards ZZZ; and [requested priority handling] with ZZZ ATC and that I needed to return to the field immediately due to losing all forward and most side vision. Oil began to stream out more quickly from the engine compartment and began to leak into the cockpit from where the canopy seals to the windshield. The engine began to run very rough; and I made the decision while on course to maintain a moderate engine power setting and start a shallow climb; attempting to strike a balance between what I knew would be very short engine life and having the luxury of speed / altitude in case the oil caught fire or the engine failed completely.Having turned back to a roughly 150 degree heading and having no forward vision; I entered a visual approach for Runway XXR into my Garmin GNX 375; which would give me the benefit of having glideslope information on my Garmin GI 275 AI/ADI. After this point; I believe that I made numerous additional radio calls of the following nature. Multiple times advising that I had no forward vision and the windshield was obscured.Reporting the field partially in sight out of the right side of the airplane. Asking the Controller for vectors to set me up on a final approach to XXR.Verifying if winds were still light and variable. Asking if there were any obstacles to be aware of between myself and the airfield.Upon intercepting a 1 ½ to 2 NM final for XXR and turning on course; I was still completely unable to see forward or ahead from within the aircraft despite the runway being directly in front of me. I believe my next and final radio call was to advise ATC that I was removing my headset; as I would need to open the canopy and attempt to gain forward vision by unbuckling my lap belt and shoulder harness; and standing up in the cockpit. With no reference to my airspeed or any other operating parameters; once I was confident I would make the airfield in the event of complete power loss; I unbuckled myself and took off my headset; lifted myself up and out of my seat by using my right hand grasping the top of the windshield; and used my left hand to continue flying. The sunglasses I was wearing were able to keep oil that continued to stream up and over the cowling and windscreen out of my eyes long enough to land the airplane while in a partially vertical / standing position in the cockpit. As I touched down; I pulled out the mixture to stop the engine; brought the aircraft to a stop; and exited the aircraft on Runway XXR. Fire / emergency crews met me as I stopped and exited the aircraft on Runway XXR and offered to provide medical aid and a check up. I called [mechanic] and advised of what happened; and he came out with some others from the shop to retrieve the aircraft from the runway. His initial assessment upon removing the spinner was that the plug that had been removed and replaced after completing the required visual inspection for AD 98-02-08 had failed; allowing oil to escape through the hole in the engine normally occupied by said plug. If the plug did in fact fail; the life of this plug was approximately 20 total minutes on the ground and 16 in flight. I was the sole occupant of the aircraft for this flight; and spoke with the Tower personnel on the phone upon returning back to the shop with the airplane. I provided them with my contact information. The Controller who assisted also informed me that I had communicated the emergency on the ground frequency; rather than Tower; which I did not know in the moment and nevertheless was provided with the same assistance.