Edelbrock 1406 whistling

I wish I would have read this earlier. As soon as he said the other carb did the same thing. I blurted out "manifold" to myself. Although the mention of "oiled paper" a little later on in the post told me it was a warped carb base. Glad you isolated it.
I went looking and found this on the back of a Gumouot can of spray carb cleaner, make your own judgement:
"WITH ENGINE RUNNING:
CARBURETOR: Spray GUMOUT® to both ends of the choke valve shaft while working choke by hand. Spray down and around the carburetor throat to remove deposits from the throttle plate area. DO NOT SPRAY DOWN CARBURETOR THROAT WITH ENGINE OFF. DO NOT SPRAY BELOW THROTTLE PLATE. CHOKE: If choke sticks, remove choke cover and spray. PCV VALVE: Disconnect the crankcase side of the valve and spray GUMOUT® into the open end of the valve while working the plunger back and forth...."

Safety is always priority. Doing anything to a running motor puts you in harms way, especially with a fan whirring 12 inches from your body, an explosive gas generating battery next to spark plug wires, and 500 degree headers slowly cooking 5 quarts of oil, as well as raw fuel in almost aerosol form out of the carb squirters, not to mention close to boiling water under 16psi running through cooked radiator hoses that may be as old as your kid who just graduated 8th grade. Lot of things can get you under there, best defense is an alert technician (you).