Shawn:
You are correct in that things are out of sync. Do the cameras take genlock? (sometimes called black burst). This is the sync signal that keeps everything in the analog world working together. On the seg, there should be a "sync in" or "genlock" connector (BNC) on the back. (One tv station I worked at had the WJ-4600b a LONG time ago). This is an input for the signal. You will need a simple black burst generator. Connect the signal from one camera thru the BG-50 and on to the seg composite cam 1 in, and then connect BB to the other camera genlock in and to the seg genlock connector. Problem solved! B&H has one by Horita for $260 (model BG-50). Here's more if you want to take a look. http://www.horita.com/. You could also try to find a legacy piece of gear rather than buy new.
Hope that helps. A bit rusty on some of the older tech, but man we had fun with some of that stuff! (If the cameras don't take genlock, then.........hmmmmm??? Could try a digital genlock unit like the Datavideo, but things are starting to get pricey. Not really sure if that would work or not. Should in theory.)
Best,
Kfox