SUCCESS!!!
After fiddling around with a second monitor, I finally solved the problem. I tried to set the resolution without first setting up the "new" monitor (a BenQ display 23") with it's native resolution. That does NOT work. What I found is that you MUST first set your alternate monitor with it's native resolution, then RESTART the computer. This way, IRIX detects the capabilities of the monitor and allows the resolutions to be in DX mode so that you don't need to log out to see the results of the change. This is important!! I first tried without following this step and it didn't work.
Once you have the system rebooted and running at full native resolution, try loading the various 1600x1024 resolutions that come with IRIX. They should work with the DCD and the 1600sw, but what I found is that there was an issue with noise in the picture. Also there was an issue with the screen going black as if it lost the signal then redisplaying the image. This happened multiple times, so I figured that there must be a problem with that mode. I tried the reduced blanking mode that Recondas posted, but it also exhibited the same issues.
The mode that WORKS is the custom resolution that Recondas posted called 1600x1024_60-1704TPPL-1056TLPF.vfo. I don't know if this was made for an analogue connection, but as far as I can tell, there are no display issues at all. One important note is that the Multilink Adapter MUST be set to "Alternate Mode" in order for the display to show up. The "Zoom" setting doesn't seem to make a difference whether it's on "Wide" or "Standard".
I have the .vfo file attached here so that you may also have your 1600sw running on your octane

One other thing to try out is if this vfo file will work on an analogue 13W3 connection as well. I have a DCD installed now and I'm not about to rip it out after all that I've been through trying to get this to work in analogue mode. Sorry. But if you have a setup like that, or are able to get one plugged in, then I think this technique of live monitor swapping might just do the trick.
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2xR14k 600MHz, 4.5GB, V12