Personally I would stay with the 10DN external regulated unit you have, but that's me. It you switch to the 10SI or 12SI with internal reg, you should stay with the three-wire as suggested.
There is a problem with that however. The F & #2 regulator wires go to the F & R on the 10DN and nowhere else. The #4 reg wire will now go to the #1 on the new SI alternator. The #3 reg wire will now go to the #2 on the SI alternator.
What I am getting at is if the problem you have now is because of wiring, you will take the problem to the new internal regulated alt. Only the F,2 to F,A wires will be removed. Nothing else changes.
The one thing I'm not sure of is what charging system was in your C60 originally?
Chrysler brought out their alternator in 1960 and put it in nearly everything they sold. GM didn't introduce an alternator until '63 and many models didn't get one until '65.
In your post above you said reg terminal #2 had 0 volts. Is the other end of that wire on the alt "R" pin the same 0 volts? Should be about 6 V.