LOL, I have since solved this problem and I actually ripped some Donkey Kong 64 videos just a minute ago (DK Rap stuff).
Apparently, I didn't know how to do this in 2020, but I've since been ripping videos from emulated games regularly, either for footage for YouTube videos, or things that I'm referring to when I'm talking about games on social media.
So if anyone else has this question...
I use BizHawk, which has a "Record AVI/WAV" function. I record video as "Full Frames (Uncompressed)", which does mean very large .AVI files that can be like a GB per minute. But it ensures that it is recording all the pixels as they should be, cleanly at native resolution.
For most purposes, I don't need them at their exact tiny resolution, so I use an Adobe Premiere Pro plugin from Autokroma, called "Visual PixelPerfect". I enter an integer under "Scale" so I can enlarge it to any size, and it keeps the pixels crisp - that is to say, nice and square, with no distortion around the edges - and then export to an H.264 or HEVC video so that I get a very clean .MP4 file.
Already that makes it much more usable and smaller than the original .AVI file. But if the filesize is still too big for social media, I use WonderShare UniConverter, and drop the file into the "Converter", to rerender it with different settings. Often what I do is have the encoder at H264 (seems to still have better compatibility with social media and apps like Discord, than HEVC), and leave everything else as "Auto" - usually there's no need to change the resolution or frame rate - because just lowering the bitrate is often enough to shrink video files down considerably with no noticeable drop in video quality. (Besides, "Converter", UniConverter also has other tools, including "Compressor", but that brings distortion into the video.)
It is still a few steps, and to improve this, it would be nice if an emulator could record video straight to H.264 or HEVC, but I guess having to convert/compress/process video on the fly while also emulating takes up too many resources. Maybe one day!