Well I hate to see you not use the alternator you bought, but in all honesty, you are going to need the internal regulated one for the stuff you want to run. The 12 SI is 94 amps and will probably work, but if it were me I would get the CS and go with the 144. It seems to be more reliable. The conversion is very simple, just follow my diagram below.
The CS needs a bigger resistor in the brown wire from the key switch which you show 4.4 volts on. You will have to resolve that to 12 volts no matter what alternator you use.
Then you run the brown wire to the L pin on the CS alternator with the resistor soldered inline. You can find the CS alternator plug off a junker,1990 or newer, or they sell the adapter online for about $25. Maybe O'riellys sells one.
Then connect the red wire from the old regulator to the S pin.
Then just run the output wire from the back to your main junction where the other red wire goes and you're done. You will want to upgrade the output wire to an 8 gauge, to handle the increased amps the CS puts out.
The CS 130 is plentiful but the CS 144 has a better reliability reputation. Check online for one.
If you have any questions just ask.
If you want to keep using the battery gauge in the dash cluster, you will have to wire the two gray (black) wires like the diagram shows. One wires to the battery positive, and the other wires with the alternator output wire at the main junction block.