Last night when I got home from work, I took another stab at getting the integrated multiswitch to work with my Spaun 5802 and was able to at least get things working well enough until I get around to fixing the LNB mount on my dish, either by removing the integrated multiswitch from the LNB mount or replacing the LNB mount with one that doesn't have an integrated switch (I'll also have to rerun a few cables in the process).
When my dish was first installed, I had tried hooking up a pair of outputs from the integrated multiswitch to the Spaun 5802 and could only get odd channels, so I abandoned it for a few days while I dealt with other things (just moved into a new house too). It turns out that the voltage switch on the Spaun was set to 12V at the factory. Switching it to 18V allowed me to hook up a pair of outputs from the integrated multiswitch and break them into 8 outputs for sat 101. This leaves me with the other pair of outputs from the integrated multiswitch that get 101, 119, and (when I get the third LNB) 110. I think that's the best I can do for now, as I'm pretty sure that the Spaun doesn't pass the tone for the 119 sat - if it did, I could hook the other pair of outputs from the integrated multiswitch and be all set.