Although I can't recall ever seeing it officially confirmed by Canon, I think the general wisdom back in the day was that the laser-matte screens with a Roman numeral in the name worked better at C.Fn-0 setting of '1', while those without any Roman numerals did better with C.Fn-0 set to '0' when used on cameras introduced before the specific screen in question.
But that may have just been an old
wives photographer's tale. You know, kind of like the "ALWAYS turn IS off when on a tripod" religion that is still being practiced in 2018 because the first generation of IS lenses back in the mid-to-late 1990s had issues when IS was left turned on and the camera/lens was placed in a tripod. Never mind that most lenses with IS made since about the year 2000 automatically sense when a camera/lens is tripod mounted and takes appropriate measures automatically, or that some newer Super Telephoto lenses even have specific "tripod modes" in the IS routines that compensate for mirror and shutter vibrations.
I don't think I ever used anything other than the supplied screen with any EOS film cameras.
Since each screen is unique in both the pattern and overall brightness allowed through to the light meter, there is no "correct" setting for the newer screens when used with older camera bodies. The older cameras' firmware does not include a setting that perfectly matches the newer screens' exact pattern and brightness of transmission. That's one reason among several that Canon recommends using only 'Center Weighted Averaging' metering with most screens other than the one supplied with the camera.
There is only the setting that is "less incorrect" than the other. The Ec-C IV seems, from the descriptions at the Canon Learning Center Guide linked in the question, to be somewhere between the screens listed for setting '0' and setting '1' listed in the EOS-1V manual. Although there is some useful information to be gained from this old discussion at Fred Miranda, the understanding demonstrated by the participants at the link is a bit naive with regard to how the custom function for focusing screens works. It's more than just a global brightness adjustment comparable to entering a +2/3 Ev EC value. It's more like using a mask in Photoshop that boosts the metering areas behind the specific etchings of each focusing screen while leaving the unaffected areas alone.
With the earliest EOS cameras, evaluative metering used very few (three?) metering segments, so there was not much difference between the two concepts. But as the light meters became more and more sophisticated and were divided into a higher number of smaller metering segments, the profiles for various focusing screens became more and more specific. The EOS-1V has a meter divided into 21 zones. The EOS 1D Mark IV (the last 1-Series EOS camera to not use an RGB+IR meter that is essentially a low resolution CMOS imaging sensor itself), used 63 zones.
The only real way to check for sure is to set it to both values and compare the metering values to an external meter (set to measure the same angle of light) known to be accurate in a controlled test of a scene with both constant (over time) and uniform (over the entire field of view) brightness. You'll need to be able to vary the brightness in very small increments (less than one-sixth stop) to find the differences in the 'breaking points' between the one-third stop step differences of which the camera is capable of metering.
I have a hunch you will find that the C.Fn-0 setting of '1' will meter a little brighter than nominal in 'Center Weighted Averaging' mode (and thus recommend a slightly darker than ideal exposure) while the C.Fn-0 setting of '0' will meter a little too dark (and thus recommend a slightly brighter than ideal exposure).
The thing to remember is that the "stock" screen with a microprism in the center that uses C.Fn-0 setting '1' is still darker overall, and particularly darker in the very center where the microprism ring is, than the two brighter screens (Ec-N and Ec-R) that use C.Fn-0 setting '0'. Most of the other optional screens, including all other than the Ec-N and Ec-R available when the EOS 1v was released, are either slightly darker or slightly lighter overall than the "stock" screen that uses the same default C.Fn-0 setting '1' as all of the optional screens other than the much brighter Ec-N and Ec-R. But none are darker in the very center where the stock screen has a microprism ring. They're either equally dark, because they also have a microprism ring, or much brighter in the center because they do not have a microprism ring. The differences in the locations and types of the etching, and thus the exact locations of the variations in brightness, is why 'Center weighted Averaging' should be used with the optional screens, even those that share C.Fn-0 setting '1' with the stock microprism screen. If, for instance, you used 'Spot' metering with an Ec-C II or Ec-C III that does not have a microprism ring in the very center the meter would read much brighter than it should and the recommended exposure would be much too dark.
There is the possibility that you will find that the newer Ec-C IV is brighter than even the Ec-N and Ec-R, and thus even a C.Fn-0 setting of '0' would still meter a bit bright resulting in a slightly dark recommended exposure, but I would not expect that to be the case.
Keep in mind that film sensitivities from one batch to the next of the same film product can vary, and certainly from one film to the next with the same speed rating. The exact strength of developing chemicals can also vary. Exposure has never been an exact science unless one carefully controls all of the variables, including the manufacturing of film emulsions and making developing chemicals from scientific grade ingredients.