Quisp,
This looks like the same ST head set up I have, your on the right track. Yes the two smaller wires were for an indicator light in the old dog house, cap them individually and tuck 'em out of the way. Just be sure they won't hang down and rub on any of the moving parts, remember, there will be some vibration and shaking so you might have to secure them.
Sounds like you have the right wires U5 and U6 are your commons and U1 and U2 will be positives for your two legs.
I verified mine before I wired it all up and put it to bed. I used large clips to hold a set of wires, U1 and U5 so they were close to each other but no contact. Did the same for the other set U2 and U6. Then I fired up the gen and used my multimeter to test the sets for voltage, it was spot on.
Finally, YES!!!! Ground your ST Head, if a grounding screw is not provided, you can ground it to any of the mounting bolts or the cover screws. This should run to your main grounding block which should also have a ground coming from your grounding rod.
I used a 10/3 fine braided wire to go from my gen head to my first junction box, the same stuff used to run 220 power to an oven. it'll take the vibrations much better than the standard solid romex wiring. I ran my ground with a separate piece of 10 gauge.
Murph'