Well you said you have the S terminal connected to the ignition and you never mentioned the R terminal. Perhaps your starter doesn't have one. If the wire you have from the S terminal goes to the coil that would give you the 12 volts for starting. I would run my coil power wire from the relay rather than from the starter just to keep it out of the heat. Maybe the solenoid has an internal resistance and is not giving full battery voltage to the starter. You can check the solenoid by disconnecting both large terminals and use an ammeter to see if there is a resistance from one large stud to the other when the solenoid is energized. You can also leave it connected and put a voltmeter on both large studs when starting to test for voltage drop across the solenoid contacts, Do not let the studs rotate when you tighten the nuts, if the studs rotate the solenoid will be ruined and you will have to buy another.
I have a Powermaster geared starter on mine, it's 464 cubic inches and 10.5:1 compression ratio, the starter spins it over quite well hot or cold. Yours should be the same unless you have a very high cylinder pressure.
Good luck.