It sounds like you have a big short somewhere, I would suspect somewhere in the ignition since it is bogging down at the same time and the alternator/charging system checks fine.
Take your car at night time to the darkest place you can find. Turn off all the lights and pop open the hood with the engine running. It helps if your eyes are also adjusted to the darkness. Look around the engine for sparks or arcing from the spark plug wires. If you don't see anything, grab onto each of the spark plug and coil wires and feel for shock. If you look closesly at the spark plugs you should be able to see them actually firing, I always could. It'll look like a ring of light around the plug. Watch what happens when you increase the rpms and keep looking for sparks or arcing/grounding of wires. Just don't stick your hand into moving parts!
You've got a big drain on the system somewhere, you just have to find it. I suspect ignition or distributor related. I'd give it a good tune up; replace the cap, rotor, points if you got em, spark plugs, wires and see if anything happens. Also, ground the engine out in a few places and make sure there is NO paint or grease on any of the connections. Sand it down if you have to, but it should be bare metal on a ground, especially the negative from the battery. You'll find it soon enough!