Ongoing problem with inconsistent filament feeding

This has been ongoing for several weeks and I've tried a number of things and I'm no closer to a solution than ever, so let me try to put it all in one place and see if I can get some new input.

The Problem

While printing, quite often the filament just stops moving, and no extrusion happens.  If you watch the filament, you see it stop moving which is not always easy to see; sometimes I mark the filament with Sharpie to see if the mark moves, and sometimes you can see the wheel on the retaining arm not turning.  If you're watching the print, you see instead of it laying down lines, it lays down only a few "crumbs", dots or flakes of plastic, though depending on the print job it isn't always obvious.

If this is allowed to go on more than a few moments, the teeth on the geared wheel will start to chew a curved notch out of the filament, causing it to get filled with crumbs of plastic, which seems to only make the problem even worse -- now the crumbs make the wheel slip more easily.

This seems to be more likely to happen on the first few layers of a print job, and if I get through those, it might get through the rest of a print job without a problem.  But that's not for sure.  Sometimes it'll happen later into a print job.  Also, note that I'm saying layers, not time.  If I am printing a narrow but tall thing, the problem only happens in the first few layers, so not for very long in terms of time, but when I print a low, flat thing, the problem continues to happen for many times more minutes than with the narrow tall thing.

If this is happening and I pause the print job in RH, then move the bed down and the head over, and click Extrude, I get a nice steady stream of filament with no other special effort required.  Generally speaking, using Extrude always gives me steady extrusion (though I do notice it seems like while the filament comes out, sometimes it comes out with a sort of zig-zag -- it looks "crinkled" like a waffle-cut french fry -- but not always).

If, while this is happening, I grab the filament and push firmly straight down, I can get the filament moving again and the print job continues, though of course it didn't put some of the plastic in which can cause problems in the print.

When I'm changing filament, I don't see anything significantly different about how much filament comes out when I'm retracting, or what its consistency is.

Note that this problem started mild (happened rarely) about a month ago (no system changes around when it started) and gradually got worse.

No noticeable correlation to humidity, ambient temperature, or other environmental factors.

Things I've Tried

This isn't dependent on filament -- I have had it with every color I've tried.  I'm using mostly Octave but I also have it with some Solidoodle and some SainSmart filament.

I usually run my extruder at 200 for light colors and 205 for dark.  I've tried running it higher and lower, and it hasn't seemed to matter.

I've done a complete tear-down, clean, and rebuild of my (stock Solidoodle) extruder, including an acetone soak for the hot end.  I am fairly sure there's no clogging going on.  Nothing came out during the clean other than filament, no dried-up or burnt-up looking bits, nothing grainy, just filament.

I have tried to adjust the tension in the spring on the tensioner arm.  As is often the case I have a hard time with the direction "make sure it's not too tight or too loose" without some way of gauging which is which.  But I've tried just about every tension level possible by this point and haven't seen the problem go away.  I also followed adrian's directions for gauging the tension: tight enough for the cog to make teeth marks, but not so tight that I can't move the filament freely while the motors are turned off.

Also at adrian's suggestion I tried a "cool clean" -- let the filament cool to 160-175 then pull it out, in hopes of dragging out any gunk.  Never got any gunk during multiple attempts at this, but since I also did the full tear-down/clean/soak/rebuild, I don't think there's any clogging, so it's probably moot.

At Ian's suggestion I mounted a 40mm fan to the front of my MK4 so that it blows on the PEEK but not on the hot end, in case too much heat is creeping up the PEEK and causing the filament there to get gooey.  I actually put it on so I can pivot it into place or out of the way, and have tried many prints both ways.  No noticeable difference, though to be fair, I think Ian intends this more as a long-term means of preventing a type of clog he thought might have been responsible (but which I'm thinking isn't actually responsible), than as a fix for any existing problem.

I've redone the Z axis calibrations and bed leveling a few times just to be sure.  (Didn't re-do any other calibrations, but my circles are still printing as perfect circles, when they print, so I don't think I have a Y axis or belt tension problem.)

My System And Settings

Printer: SD3, original recipe with Sanguinololu board.
Extruder: Lawsy MK4, stock Solidoodle PEEK and hot end, and see above about PEEK cooling fan.
Bed: Standard thickness glass with binder clips, AquaNet hairspray, stock heater, wood platform.
Case: Plexiglas enclosure on three sides; don't keep a lid on except during preheats.
Other Mods: Z-nut hugger, cable guide, filament guide, and fans on the circuit board, and that's really it.
Settings: Mostly defaults, plus 1mm Z-lift in Slic3r.
Filament: Mostly Octave, some Solidoodle and SainSmart.  Stored in a plastic case with a GoldenRod.
EEPROM Settings: Adjusted XYZ via calibration cube, but not feedrates (an attempt caused problems and I backed it out).  Settings attached.