If your engine has what I think it has for ignition, the distributor
has 2 wires going into it (yellow and black IIRC), one connected to
the + side of the coil, and one to the - side. Inside the distributor
is a "module" with 2 connectors - "C" and "B". The "B" side connects
to the coil positive, which is connected to the battery through the
ignition switch , and in most cases a ballast resistor while in the
run position.  When in the crank position, some ignition switches have
an IGN2 position, while other vehicles have an "R" connector on the
starter solenoid, which both provide full cranking voltage to the coil
when cranking - bypassing the resistor.

The module does EXACTLY what the points do in an old "kettering" point
ignition. The "C" wire grounds the coil, and then ungrounds it to
produce a spark.

With the ignition turned on, engine not cranking, there should be
something like 8.5 volts, more or less, at the coil +, and little or
no voltage on the coil - (less than 1 volt, anyway). When the engine
is cranked, the voltage at the coil + should be within a couple tenths
of battery voltage(when cranking this should be between aprox 9.5 and
12).

As the engine fires when cranked, it's pretty obvious this voltage is
not your problem.

Now, the NON CRANKING ignition voltage - don't just trust a high
impedence digital voltmeter. Put a test light from the coil + to
ground - it MUST light. If it does not, the ballast resistor or the
circuit feeding it is dead.

The fuel injector pump is controlled by the computer through a relay.
If this is not working correct the car may act the way you see,
according to the manual. If you think the problem is power missing
from the coil after the key switches from the start position then why
don't you eliminate the ignition switch? Just wire from the positive
post on the battery to the coil. As far as switching to points type
ignition a better choice would be to find a module that's made to
eliminate points in a points type ignition and replace your module
with that one. Make sure it's triggered the same as yours. Also, make
sure the computer is not varying your timing. If it is, then any
replacement ignition needs to be isolated from the computer. Points
type ignition, while simple, is less reliable than electronic. I
suggest that if you absolutely have to replace the ignition with a
popints type then go to the wreckers and look at older mitsubishi
distributors. I doubt you'll find one though.
ERS

If you are hell bent on installing points, look for an older dodge
colt or Hyundai pony or excell. They all used Mitsu stuff, as they
were mitsu engines. Toyota used Nippondenso,and most nissans were
Hitachi.

Bet if the critter was within 60 miles of me it would be running in
less than 2 hours, including driving time.