However, I seized on the FFmpegX comment as a route I could take as a practical experiment and found Handbrake, which I am now getting a little familiar with.
HandBrake is an excellent app. It provides presets which the novice can use to target specific end use encodes, as well as, provides manual control of specific settings and features likely to be employed by advanced users. I use it regularly to create H.264/AAC/AC3/Chapter and H.265/AAC/AC3/Chapter content for my iTunes library, websites and macOS, iOS, and/or tvOS devices.
I will try now a proof-of-process and produce a DVD with the MP4 converted through Handbrake and see where that lands me.
Since HandBrake does not have the built-in "Optimize for CVD/CD-ROM" setting previously mentioned, you may wish to start out by running tests in the single-pass, average bitrate mode. What you really want is a constant data rate that matches the data read/data throughput capabilities of the slowest DVD player on which the optical disc is to be played. Unfortunately, video content data rate requirements can vary drastically depending on the graphic complexity and resolution of the subject matter. The HandBrake "Constant Quality" setting allows the data rate to vary as high or as low as needed to achieve the constant level of quality you have selected. The "Average Bitrate" setting tends to do the same thing but employs negative feedback to "limit" changes in the data rate and thus tends the reduce instantaneous data rate excursions. This may sound like a lot of gobbledygook, but all it really means is that you must determine how fast your DVD player can play your video data from the disc and then encode your files so that your video player isn't trying to play the videos faster than your DVD player can read the data.
My first question though is that the total file size is radically different -- the on .mov was 3.87GB and this mp4 is 165.9MB. Does that mean I'm losing a lot of quality?
That really depends on whether the MOV file and the MP4 file were encoded using the same codec at the same resolution using equivalent settings. Basically, different codecs have different efficiency ratings. In this case, if both files were encoded as H.264 video at the same resolution, them my guess would be that the combined total AV data rate of the MP4 file is only about 1/23 that of the source MOV file and has probably lost most of its visual quality. On the other hand, if the MOV file contained DV/AIFF compressed data or AIC/AIFF, then the MP4 file could well have little or no loss in visual quality since these MOV codecs are "low-efficiency" while the H.264/AAC codecs are more modern, "high-efficiency" codecs.
One concern is maintaining whatever best quality I have in the archiving process, if that mp4 is to be the archiving "standard" format.
I tend to consider H.264/AAC to be a distribution format unless you are encoding the material at AVCHD/BD quality levels. I was referring to Apple ProRes422 as an archival/intermediate editing video compression format. It basically replaced AIC (Apple Intermedia Codec) as the "poor man's" archival/intermediate codec and is now included in all macOS releases since Mavericks. It won't improve the quality of legacy video content being updated but should, in most cases, prevent further loss of quality while providing compatibility with modern QTX-based apps. It's major disadvantage is that it is an extremely low-efficiency codec creating huge files but does support UHD resolutions up to 8K which most non-pro users aren't even worried about at this time. You must decide for yourself which codec is best for archiving your file content and at what level of quality.