What type of hive would be best for Sheer Total and Utter Neglect?

Well, I HOPE to have some interesting & positive results to share. Might be just killing more bees in ways I haven't encountered yet. Will report successes & failures. Will need some time after spring for the "normal" bees to ramp up first.  

I am becoming increasingly convinced that the single best step we can take for managing bees in a sustainable way is to proactively make splits from our best colonies each spring. Everything else seems to be peripheral low value stuff by comparison.

I'll outline in the context of my own beekeeping:

1) I overwinter approximately 12 full sized hives.
2) Each summer I make splits from my colonies, using queen cells from my best few hives.
3) The splits get put into 6 frame poly nucs (highly insulating) and allowed to build up until autumn.
4) They get checked in late autumn to ensure they have stores - I give them a frame or two of capped honey if they are short, from another hive.

Over winter I invariably lose some colonies. But the nucs are there ready and waiting.

Over a few years of doing this my stock has improved - my losses are about the same, but more colonies are strong and healthy in the spring. This method allows me to ignore the mites - if I lose a colony or two it doesn't matter. I also rarely feed; but this is as much to do with whether you take too large a honey harvest or not.

So this is not really a "STUN" technique, but it lets me ignore all of the other worries that beekeepers seem to have.

Down through history, monks kept bees as a part of the food production for their monastery.  I visited ancient cave churches in Cappadocia Turkey, where monastic orders were first established in the 3rd and 4th centuries, and then continued for over 1500 years.  You could see how they created hive space in their caves, with little holes where the bees would enter and exit.

Their technique/strategy was to make their hives out of wicker -- basically, they were baskets.  Google "Bohemian beehive".  The hives were cheep and easily constructed, and also highly combustable if they wanted to burn them.

Every summer, they'd split their best colonies and start new ones, and every fall, they'd take the worst colonies, remove all the honey, and then would burn the hives (bees and all).  Basically, they would cull the poorest performing hives from their group and start over the next year.  It was a kind of forced darwinian natural selection.  If you do this year after decade after century, you're going to end up with only the strongest and most productive bees.  

The honey bees we have today are the biological off-spring of those old monastic bee colonies.  

Every summer, they'd split their best colonies and start new ones

Still a very good idea to do that. Genetics aside ... worst case you can easily replace winter losses. Best case you can expand the bee yard each year or just sell the extra bees.

Simply ran out of time to install some in logs this year. Did let several swarms, well, swarm up there in Sasquatch mountains though. Logs will be a high priority item next spring. Stay tuned.