Replacement screen or just the picture tube? Mine has the same issue. I'm crossing my fingers that it's the transistor for the red circuite on the neck board. In my case I fiqured it needed to be capped anyhow so I just ordered a cap kit and color transistors and some other bits and pieces and just decided to replace it all and see what happens. It's all appart now and I'm just trying to find time to get back to it.
I got a LCD replacement. The old tube was burned in pretty badly and it was a pain hauling it up and down stairs. You might want to try cranking the "red cutoff", if the screen is good, at some point the picture should have an overall red appearance. If not then you might have something in the boards on the monitor.
There is a resistor ladder for each color on the game board with a shift register I think. I don't remember the exact chip. I would double check that you are sending red to the monitor before investigating the monitor.
So what should I be looking for on the red output from the board, an AC or DC voltage or a particular waveform? The rest of the circuits have been easy to diagnose as I check continuity, then check for the proper voltages. The chips in the monitor output circuit I'm less familiar with.