Hi Doug,
I'm running a Bosch gear reduction starter (modified Oz Holden 3.8L V6). Most pre-engaged starters' solenoid coils pull more juice than the Mini start circuit can supply, as you suggest.
On the advice of my supplier (an auto electrician) I have retained the Mini solenoid, but use it only to power the coil of the new starter. So the main power cable to the starter is now piggy backed on top of the battery cable at the Mini solenoid. This avoids adding voltage drop to the starter across the Mini solenoid. A feed wire goes from its `starter' stud to the spade lug of the new starter.
It cranks the 1360 fine now, even in cold weather, with 11:1 C/R, electronic ignition and 20deg static timing.

Doug are you talking about the little nut/bolt here.

Or...

Leave your old solenoid in place and wired exactly as it is now.  Run your old starter motor cable to the new starter motor threaded lug.  Make a small jumper wire that goes from the threaded stud on the new starter to the "trigger" spade lug on the starter motor.  That allows you to use your existing solenoid as a giant relay to power the new motor and provide the trigger for it at the same time.

You want a large wire headed to the main lug on the starter, same size as the wire from the battery to the old solenoid.  You want a quality relay on a proper relay block such as you could buy from a truck/tractor heavy duty parts store or get from a friend and you want that relay to send power to the trigger lug on the new starter.  The ignition switch alone is not sufficient.  You can remove the old solenoid and use an exhaust mount bobbin as the point where all of the +12V connections meet up, but not a solid bobbin!

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Do I take the wires on the front terminal and attach them to the large terminal and the small wire to the tab in the black plastic housing?

Can anyone give me a tutorial on which wires on a standard mini solenoid go where on these new starters?