[kdjones2000]

That should be the stock connector for no alarm.

Seems to me that you have covered many bases already.
1) You did the Clark's plan and it checked out, but what about the DME Test Plan?
2) Computers rebuilt, so injector drivers *should not* be the issue. I assume from above that after it cut out, that it still would not start if you unplugged one of the injectors? What happens if you jump the DME relay?
3) What about fuel flow? You checked pressure, but is the pump flowing enough?
4) One experience I have had with these cars is that if the speed sensor is too close to the flywheel or gets damaged, that the engine can cut out and you get a no-start until it cools down. Re-check your gaps and condition of the sensors.
5) It could be that the injector harness may have something going on, but I guess you already replaced that. These engines get HOT, and wiring gets brittle.
6) When it is in no-start mode, are you getting tach bounce? What about spark? Looks like you have already checked the distributor/rotor and replaced the coil.
7) This is an '87, so the airbag module also plays into the DME relay activation. Is the connector to the orange module up behind the glovebox connected securely? There is a way to jumper out the airbag module if you want to try that.
8) I have also had the situation where the tines on the pins in connector to the DME were spread out, making no or intermittent connection to the DME. Take your ohms/voltage measurements from that connector; that way you know what the DME is actually reading/seeing.
9) When it is in no-start mode, have jumpered out the KLR and see if it ran?

Good luck...