It sounds like a Vacuum Leak:Common areas are what you posted & also the Vacuum Booster, Vacuum Modulator & also Vacuum Advance.If all checks good, I would want to check for late Valve timing / or adjustment via Vacuum Guage
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No Valve Cover would not have that much to do with it.
You stated that you had Power Brakes...There is a Vacuum Booster behind the Master Cylinder if you do, if not, there is no Power brakes.
You stated you have Automatic Trans....There should be a Vacuum Shift Modulator on the side of the Trans.
You can close off all Vacuum Ports, including Vacuum Advance & check for internal Carb Leak with Guage