I work as an electrician, It sounds like your old flicker problem has to do with a loose connection in the circuit somewhere, like an under tightened screw or poor wirenut splice, or connection in the panel like Stangbat mentioned above. Such problems are not unlike old and worn out connectors on your boards. Those back wired outlets where you just push the wire in the hole are junk and notorious for such problems, under heavier loads they loose their grip and conductivity. I always use "spec" or commercial grade receptacles as they hold up longer and "grip" the prongs tighter.
If you have six machines I would recommend four or more duplex receptacles on that one circuit. gives room for expansion and eliminates need for splitters or powerstrips.
