Same here, Every October or when the weather turns bad I change my 2002 Trans Am WS6 and park it till May. I am using Amsoil 10W30 100% synthetic. I NEVER start the car once its parked. Some just can't resist running theirs once a week or so but thats the worst thing you can do. Moisture forms in the engine and exhaust system leading to more problems.
For 20 yrs I had a 1964 Impala, did the same thing with that car and it always started right up in the spring. Only thing that was a problem on that car was battery's, At only about 1000 miles a year they never seemed to last beyond 3 yrs even though I would place a 2amp battery charger on for a week or so to build up the battery before firing it up. I never once added a thing to the fuel tank and never once had a problem. Sometimes if you listen to all things people do to there cars, its a wonder the even run. If you have to babys sit a car, you need to get a life.