"This doesn't look like an alternator or weak battery problem to me."

Actually, it does.

You need to make some measurements at the battery using a good DVM:

- A fully charged battery (engine off) should be 12.6 volts, or thereabouts.
- With the engine idling, battery charging, battery cold, around 14.5 volts, or so.
- As above, with battery warm, around 13.5 volts, more or less.

Much depends on the battery's condition, state of charge, temperature, other electrical loads, and so on.

Whether or not your problem is a bad alternator, bad ground, worn brushes, bad connection, bad regulator, or bad engine harness -- or a combination -- your symptoms sound very much like low system voltage.
--
Don Foster (near Cape Cod, MA)