@ArcadeJason,
Did you mean the modulator circuit? Color burst is done inside IC A2
Wow that schematic is gross!

(and incomplete) But it gives some hints. Thanks for posting it!
I don't remember if my AVM came with a manual or not. I think it did and the schematics are in there I'm pretty sure.
I don't know where the thing is though. Buried someplace.
I agree, an external demodulator is probably the
easiest path. If you can find one that works with the AVM's signal and with the monitor's input type that will be the quickest solution.
@prOk,
If you have an oscilloscope you can probe around looking for the pre-modulator video signal. If you find it try just connecting the RCA center conductor wire directly to that signal. Shield of the cable would go to system ground...you can get that from anything connected to the RF output barrel.)
If you don't have a scope, try connecting the RCA signal wire to the node that looks like a summer output going to the modulator.
I can't really read it, but I think R4, R7, R27, and R32 share that connection. If you get anything visible on your composite monitor that's a good start.
If it's "good enough" you're done. If not, you'll need a video buffer amp to boost the signal. Even if it's good enough you should add the amp to protect the AVM and to help your monitor deliver a good picture.