OK, it still doesn't work, but I have it narrowed down to the chip...
From another member on Sega-16, I constructed this circuit prior to running the composite signal into the LM1881:
Connect them in series and wire them like this:
Gnd --|===|--#--|===|--- CSync
680 | 10k
|
|---||---ยป LM1881 CVideo input
.1uF
LOL @ ASCII schematic :V
Take care, I edited this message like 4 times :p
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I purposely left the leg on the 10k resistor connected to composite uncut and when I connected it directly to the composite out, it stabilizes the picture, but the colors are all out of wack. I tried to take a picture and video, but it doesn't come out the way I see it in person. Anyway, I'm fairly sure that the CXA chip is the culprit, as I can get a solid sync signal from the EXP port, the C6260, and from the composite out on the EXP port, as well. So, what I'm going to do is I'm going to order a new CXA1645 from a stateside dealer and just redo the entire circuit. This may take some time, so I'll check back in once I get that done.