If the compression is that good when cold, I would question whether burned or stuck valves is the problem here. It certainly wouldn't hurt to check that out, though. However, I'm also leaning more towards an exhaust leak of some kind. Besides checking the exhaust manifold gasket, the manifold itself may have developed a crack around back, where it's hard to see. This is quite common. They never seem to crack on the front side, where they're obvious. Since the car is new to you, there's no telling YET what problems there are with it in terms of inferior parts. This is no reflection upon the previous owner, but a lot of garbage parts from the 1970'-s through early 1990's have found their way onto our cars simply because the quality and availability of quality parts were not there until the larger vendors stepped in and helped straighten this out. It's very likely that the exhaust manifold clamp is a J.C. Whitney or Rick's Auto off-shore piece of junk that didn't fit properly from the git-go. Perhaps with the cheap-*ssed mufflers available until a few years ago with their very thin flanges, the cheaper clamp would work. But if the former owner installed an Aires muffler (doubtful) or new exhaust manifold (even more doubtful), these older clamps will NOT fit! The flanges on both the new mufflers and exhaust manifolds are closer to the original diameters and thicknesses, so the thinner older clamps can no longer hold the pieces together properly, resulting in leaks. I have had to replace such parts probably 5 times in the last two years on customers' cars after installing either a new muffler or manifold, or both. The newer clamps available from the vendors are much more substantial and do an excellent job of maintaining the fit and alignment of these parts.
To check, put a floor jack beneath the large swell of the muffler near where the pipe to the manifold comes out. Then remove the clamp. Back the pressure slightly off the floor jack so that the muffler flange can be properly positioned against the manifold flange. You may need to loosen the tailpipe clamp on the frame to do this. Once you're sure the pieces are sealed against each other, start the engine, without the clamp (that's why the floor jack is there). If there is still leakage and popping upon revving up the engine, try moving the pipe around on the manifold flange to find the "sweet spot" where it seals. If that doesn't work, I'd look for cracks in the manifold or a bad gasket. I would suspect that the popping is more pronounced when you back off acceleration, right? That's a sure indicator of an exhaust leak.
Before you remove the clamp to either test or replace it, ensure that the opening between the two halves is not directly facing the carburetor throat. If there is any leakage whatsoever at the muffler and manifold juncture, the exhaust will spit out under decompression and blow into the carb, causing popping. Loosen the clamp bolt nuts and rotate the clamp so that the opening between the two halves points as far away from the carburetor's throat as possible. That alone may solve the popping problem. But you'll still have to deal with what's causing the leak in the first place, which probably brings is back to the clamp or gasket. If you hear a ticking noise, it's most likely the exhaust manifold gasket. If it's more of a muffled roar, there's a crack in the manifold. Judge your actions accordingly.
By the way, should you remove the exhaust manifold to check for cracks, run a TRUE straight edge across the tops of the four ports. They must be in near perfect alignment. Most likely, #4 port will droop as much as 1/4" lower than the other three ports. That means it's warped. VERY common. There are ways of repairing it, but the jury is still out whether the manifold will retain the repaired position or droop again. With a droop in #4, it's almost impossible to get a good seal here. That will cause exhaust leak noise. You could use the heavy cardboard gaskets that are more forgiving of warped manifolds, but they tend to blow out fairly soon under such circumstances. The new exhaust manifolds are excellent and align perfectly with the gland rings and gaskets.
Well, this gives you plenty to check. Rest assured, the Model A didn't come from the factory with the symptoms you describe. There IS a problem and it CAN be fixed.
Marshall
