I have been chasing an off idle stumble in my 57 Cadillac for like two months. Rebuilt everything to factory stock on the motor and still thing has terrible off idle stumble and no power at the top end. Got pissed today and pulled the air-bath air cleaner and started tuning the car and realized no ****** stumble. Drove the car without it and I swear it picked up 3-4 seconds to 60 and no a single off idle stumble to be found. I washed out the oil bath in solvent when I got the car and let it dry for a few days before re***embling it. Is it possible that this thing is so clogged up that it would restrict the airflow that much. I have seen this in the past with those terrible helmet style cleaners on my strombergs but never on something setup like factory. I thought these things were unclog-able.
Have a look at it. It should be full of a hair like substance. All you need to do is swish it around in cleaning solvent and let drip dry. After all this time if it was never cleaned properly you may want to soak it over night. Do not blow it with an air hose, that can make channels that reduce its effectiveness. If the filter is not clogged or damaged it should not affect performance. Use 50 weight oil, light oil can slosh around and get ****ed into the engine. Fill only to the line indicated. I don't know what else to suggest. The only thing that comes to mind is that somehow your carb is running too rich but even then the difference should not be as dramatic as you say.
Actually cutting up the oil-bath to use a modern filter inside this weekend, but there are like 100 threads on Cadillac 365's have off idle stumble and nobody reporting back what fixed it. Secondaries are also opening correctly now with better timing.
Mine has an AFB carburetor, I chased that stumble all over the map and finally pulled the oil bath and replaced it with a paper one. Still had drivability problems, mostly vapor lock and hard starting due to fuel boil. When I installed an electric fuel pump and regulated it to less than 3 PSI all the problems went away.