Coaxial Switch Using Arduino and Multiplexers
I bet you didn't buffer the output.

If you tried to direct drive your 75ohm load, you would  discover a lot of attenuation from the 250ohm switch resistance.

Use 10K load or so and buffer the output with a 75ohm line driver or whatever you can buffer with 10MHz BW or so.
Consider how critical your levels need to be and matched source impedance to 75 ohm. Ideally everything sourced to your monitor is 75ohm for NTSC composite video.

I hope that works and my intuition is correct.