Could be the ignition switch. Have you replaced the coil? A coil can be intermittent. Points ignition is pretty simple - my advice would have been to get it running reliably with the points distributor. You have made things considerably harder by introducing new components and wiring to a system that already has a problem.
I suspect the junkyard genius diagram has an error. I will explain below.
The circuit for the Duraspark modulehas a lot in common with the points ignition circuit. Look at the diagram and let me point out what's connected where. You need to use the diagram and also understand why its connected that way.
The running circuit - 12V is connected to the coil through the ignition switch, via the resistance wire. The resistance wire limits current through the coil, since the coil and module cannot stand too much current for a long time. The green wire turns the coil on and off by alternating between grounded and floating (connected to nothing - "floating" in mid-air). Inside the module is a big transistor that the module electronics turns on and off, just like the points open and close. The module is simply an electronic replacement for the points - it does nothing to change the intensity or duration of the spark.
When starting, the resistance wire to the coil is bypassed, so that the coil gets full current. This makes a stronger spark when starting. Power comes from the "I" terminal (ignition) of the starter solenoid, and goes to the coil. This should not connect to the module. Module power should be a separate wire that is powered during starting and running.
Let me point out what each wire to the module does.
The red wire is the module power. It should be at full battery voltage during starting and running. Connect that to the red wire that originally went to your Prestolite module, not to the red coil wire.
The white wire is a logic signal that retards the spark during starting. It is correctly connected to the blue "start" wire from the ignition switch. By connecting to the "S" terminal of the starter solenoid, the blue wire turns the starter solenoid on to run the starter motor. The starter solenoid also has the "I" terminal (ignition) that can be used to power the ignition during starting.
Some starter solenoids do not have the "I" terminal. If that's what you have, I suggest you get a new replacement that will come with the I terminal.
The green wire controls the coil. It is alternately grounded and floating, depending on the magnetic VR signal from the distributor.
The black wire is a ground. As shown in the diagram, an extra ground connection to this wire (in addition to the connection to ground at the distributor) can only help.
The orange and purple wires are the magnetic VR trigger signal from the distributor. They are polar, so violet must connect to violet, and orange to orange. The original wiring is made so you can't get the polarity backwards, but if you are wiring the module yourself, be sure to get the polarity right.
If you are going to copy a Jeep diagram, I suggest you use this one -
http://oljeep.com/gw/elec/78/78_FSJ_Wir ... mPage7.jpg - this is the 1978 diagram, and should be very very close to the factory wiring for your '77, except using the Motorcraft ignition instead of the Prestolite. It will also have a resistance wire for the Motorcraft module, which the Prestolite ignition does not use. Use a ballast resistor in place of the resistance wire. Here's a suitable part -
http://www.rockauto.com/en/moreinfo.php ... 65&jsn=427