Downloaded the Service Manual for your TV and spotted the RGB lines straight away:

There's a very good chance your TV can be modified for RGB input.

The idea would be to apply a voltage (say, 1 volt) to the blanking pin and cut the OSD traces to insert the NES RGB output. You lose the OSD display (e.g. volume slider, channel indicator, etc.) but gain RGB. In my builds, I install a 4 pole relay so I can easily flick back to adjust contrast and brightness using the OSD and TV remote. Works a treat!
Sync would go straight to the composite video input. Easy. Does your TV power on to AV mode?
That's the high-level overview.