Took me a little bit longer to get to than I planned, but I finally got the capacitors replaced. The diameter of the 820 μF capacitors were a little larger than the original ones, so it was a bit of a tight fit getting the three of them in. While I was in there, I replaced two other 820 μF capacitors in the middle of the board even though they still looked in good shape. Thought about replacing the 22 μF and 47 μF capacitors, but decided not to. There were a lot of surface mount components near the 22 μF cap and I didn't want to get the soldering iron too close or accidentally solder where I shouldn't.
Took me a bit of time to remember how everything went back together, but I got the monitor reassembled and brought it back to the computer. Plugged it in, turned it on and was rewarded with the monitor telling me it was trying to find a signal source. Reconfigured the computer for a second display and up it came!
Monitor is fixed and now I'm back to a dual headed system.