So, for anyone that's interested how this turned out, I was able to dig up the service manual for this player, and located the analog video signal that happycube was describing (pin 22 of IC500 digital video processor, helpfully labeled "V2" in a box on the board).

I decided to go for broke and soldered a wire (30awg insulated) to the pad for this pin, and connected it to a newly added panel mount RCA jack on the back of the unit.

And what do you know, IT WORKED! Comb filtering artifacts are greatly reduced if not totally eliminated when connecting directly from this new jack to the TV. All features of the player seem to be retained (digital memory, etc) except for the "picture enhancement" which was completely useless anyway.

I hope this ends up being useful to someone else with a CLD-D606 or CLD-D604 (I presume it would work on this player also, as it's functionally the same as the 606 except with no karaoke).