Among my 57 Fords I also have a 57 Continental Mark II. It is just a BIG FORD. I had it out the past few days and was driving and running great. Then while driving through town, when I would take off from a stop it would have little power and ping like crazy, once up to speed it was fine. Drove it the next day and it did it cold as I was pulling out of my garage, then again once going down the road it smoothed out and hasn't done it again. Vapor Lock?, bad Gas? maybe weak accelerator pump????????? Every time I take it out I always put fresh fuel in it. Chevron Supreme but only 91 octane here in San Diego.
Bob, what is the type of carb and vaccuum line the Lincoln has? it sounds if it could be a slightly loose vaccuum line fitting (w copper tubing). they are most probably the type with sealing double cones, no? They often are coming slightly loose, preventing the vacc diaphragm (timing advance) working properly.
I wouldn't panic yet. Wait until you can run almost all the fuel out and get a complete new tank full maybe from another station. I had the same problem with my Mustang not long ago, on 91 its fine on 89 it will start to ping under a light load and this tank of 91 was pinging. The next tank full it was back to running normal. My friend Dave drives a tanker delivery truck and I know for a fact that whats suppose to be in the stations tank isn't always what it is suppose to be, it happens occasionally by accident. And between the Ethanol, and Calif blend hard telling what we may get at the pump :005:.
You mentioned two things that caught my attention, from a stop and pulling out of garage. Both under load were as DJ mentioned, vacuum leak.
I will check any and all vacuum lines. The carb is not the funky old teapot Holley, I believe it is a Carter.