So it sometimes happens that when I research stuff and don't find anything, I ask the question on a forum, in this case this forum. And then, while I'm killing time waiting for an answer, I stumble across all the answers I'm looking for.
So to anyone in the future who wants to know more about these strange connectors, here you go:
They are called Sure-Seal connectors, and they were (so it seems) created by ITT-Cannon some time ago, maybe in the '70's, and are still made and available to this day. In 1996, a spin-off or licensee company called Sure-Seal Connections was born and also started making this same connector series. These are specifically designed for automotive and other industrial use where a highly sealed, low-cost connection is desired in a dirty, high vibration environment. And anyone who has separated one of these connectors in their 32+ year old engine bay or fuel tank cover knows how effective they are.
The pins and sockets insert from the rear (wire entry side) of the connector body using isopropyl alcohol as a lubricant and a special tool (automated tooling is also available for manufacturing) is used to press the assembled wire/contact in. It looks similar to, but way more beefy than, a D-sub pin tool. A removal tool is available, but reportedly not absolutely necessary. The published removal procedure is to "gently" grab the wire and steadily pull it out of the back of the connector. Connector pins, boots, bodies, clamps and some tooling can be purchased directly from Digi-Key or Mouser. Contacts are available in stamped or machined styles, crimp or solder cup, with tin, silver, or gold plated versions available.
As far as the insert tooling goes, even the hand tool is ridiculously expensive (no surprise there, all tooling sold by the connector manufacturers are frightfully expensive), but I'm confident a workable alternative insert method can be found. They suggest holding the connector in a special block while you insert the pins, but that can simply be a piece of wood with a counter-bored hole in it.
Oh, by the way - the small rectangular 4-pin connector in the picture is for the ABS system (I don't have that).
More information:
ITT Cannon Sure-Seal Catalog (pdf)
Digikey Circular Contacts - Sure-Seal search results
Mouser Sure-Seal product search results
PEI-Genesis Sure-Seal Info