Tonight I did the rewire of the dome power to provide 9 volts to the dome's electronic components.
First, I soldered the batteries in series.
Then, I tested the wire-up to ensure I was getting a good 9 volts. 9.20 volts, to be precise.
I reattached the battery holders back into the dome, and hooked up the wiring, and all was well. In fact, R2's dome has never looked better. The lights were nice and bright, and I expect the time between battery changes to be much longer now.
I still have a couple more updates for R2 in mind. His outer foot shells are a sagging toward the middle of the body, which makes him look pigeon-toed. I know what I need to do to fix that, and I hope to get to that relatively soon.
I also want to have his utility arms open via remote, and eventually spray mist from behind the top arm. Those updates are probably a bit further out though.