Another thought. When the ignition is switched on with the engine hot, the fans come on. Not so with the engine cold. Could be the amp draw from the fans is diminishing what's available for the starter.
Since I don't recall this particular complaint back in the day, it could be I have a weak starter which is susceptible to this. It came with the car and the seller provided no service history, so the starter's provenance is unknown.
BTW, the battery is new and huge.
Still looking for answers to the questions above.