Frustrating charging system issue, 2000 GC

It's a 2000 Grand Caravan 3.3L, high mileage.

The charging system seems to be failing intermittently but
increasingly. Things will be fine for several days then I'll get a
battery light (low voltage) and then the car will die as the voltage
continues to drop.

Replaced battery and checked the entire charging system (passed all
tests with alternator putting out good voltage and amps) but ran into
the same problem a week later when the new one discharged.

During one of the "events", I measured 11.5V and dropping running at
2K RPM (and only slightly less turned off); took this to be an
indication of a bad alternator. Yesterday I took the alternator out
(and what a job that is) and brought it to the parts store, where it
passed their test with flying colors. Put that alternator back in,
cleaned and tightened all battery connections etc. and immediately got
14V into the battery. Hooray.

Of course this morning I am back to the battery light being on and no
apparent charging all day (less than 10V upon returning home).

So, after a bit more research, I am left with these possible theories:

1. Bad body control module -- the voltage regulator is apparently
integrated into this computer (!) and if it is bad it could be
preventing the charge from reaching the battery.

2. From a glance at the Haynes book at the store there appears to be
an "MDS relay" (I may be misremembering the name here) between the
alternator and the battery; no relay by this name appears to be in the
main relay center next to the battery and the relays under the dash
are unlabeled. If anybody can tell me where to find this relay I can
have it checked.

3. Grounding problem, probably to the computer module. The ground
connection to the battery is good; not sure how to proceed with
checking this.

4. Truly bad / intermittent alternator -- I've never heard of one go
intermittent in this way; a replacement is a nonrefundable $180 and I
hate to shotgun without knowing.

5. Bad (brand new) battery -- don't think this can be it, since it
takes and holds a charge from a battery charger, and runs the car for
a reasonable amount of time before dying.

Any other ideas, or ways to narrow this down. I am tearing my hair
out here and the cost of sending an electrical gremlin to the shop is
scary.

Thanks

JGM

If it stays off all day, it would be an absolute breeze to troubleshoot if
you knew how it was supposed to be. Since it works sometimes, that should
be easy too. Take some baseline voltage measurements when it is working.
Take the same measurements when it's not working.

Using that, it should be extremely easy to isolate the problem at the
alternator. In other words, either the alternator is STOPPING or something
else is TELLING IT to STOP. You just need to know what each wire on the
alternator is for. If you have a shop manual, again, this should be no
problem.

I wouldn't pull my hair at all until I'd figured out what component chose to
shut down the alternator.