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Is it a coincidence that 1.3Mhz at -3dB is the standard chroma bandwidth for NTSC, and it just so happens that a basic (-1/4, 0, 1/2, 0, -1/4) FIR filter with a sample rate of 14.32 Mhz gives a -3dB level at 3.58 +/- 1.3 Mhz?

Yes.

You can painstakingly work out the math longform if you'd rather. Nothing magical will show up about a number that works out to very approximately roughly Fs/11.

Is there possibly some special relationship between the sampling rate—4x the colorburst frequency—and 1.3MHz? Yes, that I think might be deliberate. But your choice of discrete-time filter? Absolutely not, discrete-time stuff was basically not a practical option during NTSC's genesis.

This thread has turned into a "ask questions about analog TVs" thread.

Is there any research about the SNES's RF modulator circuit? I know that most composite encoder chips have a max of 133 IRE, and RF has a smaller range of 120 IRE. Does the SNES in RF have a smaller chroma amplitude, or does the SNES clamp yellows and cyans?

Connecting my oscilloscope directly to the RF output of various things. No cart, so solid screen and no sound, scope set to 250MS/s and 50mV/div, the lowest setting that's not additionally bandwidth limited.
NES-001, channel 4:
Primary video carrier image at 67.25MHz; ≈-47dB during vsync/hsync/blanking and ≈-54dB during whatever color it randomly chose.
Audio carrier visible at 71.75MHz, ≈-65dB
Extra modulated signal visible at 62.25MHz, comparable in magnitude to the audio carrier.
Main 21.47MHz system clock visible; ≈ -65dB

NES-001, channel 3:
Primary video carrier image at 61.25MHz, ≈-45dB and ≈-53dB as above
Audio carrier visible at 65.65MHz (should be 65.75), ≈-61dB
Extra modulated signal visible at 66.65 ≈-68dB
Extra modulated signal visible at 56.70MHz, also ≈-61dB
Main 21.47MHz system clock visible; ≈ -65dB

SNS-001:
Weird ringing even when no power adapter plugged in at 66.75MHz, regardless of RF channel setting. ≈-64dB. Image disappears if via RF switch and console is off.
SNS-001, channel 4:
Primary video carrier image at 67.25MHz, ≈-46dB
Audio carrier visible at 71.75MHz, ≈-64dB
Extra modulated signal visible at 62.8MHz, ≈-61dB

SNS-001, channel 3:
Primary video carrier image at 61.30MHz, ≈-44dB
Audio carrier visible at ≈65.80MHz, ≈-60dB
Extra modulated signal visible at 56.80MHz, ≈-59dB

Unfortunately, the SNR of my scope isn't good enough to see anything quieter, and the whole FM radio band is coupling into everything.

I've been looking at docs for ntsc encoder and decoder chips and something I noticed that most of the "1.3 Mhz" chroma filters have zeros at ~2 Mhz, which is a much faster roll off than either Gaussian or Hamming filter. Does this mean there's chroma ringing on these filters?

Depends on the specific transfer function, whether it's continuous time or discrete, and what you mean by "2MHz".

Oh, of course. And zeroes never cause ringing, only poles do.

Is there a limit to how fast the roll off without ringing?

Not really.

Just increased group delay.