You say it's not really a vibrating sound though I would still be inclined to say chain binding or chain flutter. The low rumbling sounds like BB problems. What construction is your BB (cartridge, sealed, or cup&cone)? If taking the rest of the drivetrain apart (even taking the cranks off) and putting it back together doesn't help, then I would look at your BB.

I suppose you could proceed to the top of a small hill, remove the chain and coast down (be sure you have a brake or can employ your hands or feet to stop, obviously) and see if you get the noise when not pedaling.

The advice above is good too. Try to figure out what the triggers are.

Oh, and low maintenance...Sure, sometimes. Sometimes you spend all your spare time diddling. See, you have nothing that soaks up the imperfections, no derailleurs, no tensioners, nothing. So you feel it all. Now you're questing for perfection. But once you get that perfect setup and everything's dialed in, you can ride that for months before you need to touch it.