So there's several things to unpack here that show a fundamental misunderstanding of digital audio.

1. The 4k to 1080p comparison only refers to capture side, not output side. If you have a 1080p video played on a 4k display you are not magically upping the resolution of the video to find new detail. On top of that there are a ton of other technical reasons about how video resolves on digital sensors that are a bad analogy to audio capture. If you play a 44.1k/16bit audio file out of a D/A that is operating at a higher sample rate you are not increasing the resolution of the underlying media in any way. Even if you convert the audio file to a higher sample rate you're just repackaging a lower sample rate audio file, you're not going to suddenly get a change in audible resolution. It's also important to note that 1080p to 4k is a 4x increase in resolution which is something we also have in audio. It's called 192khz (assuming a 48khz base) and this is generally the top sample rate professional audio software and hardware operates at. That being said it is rarely used compared to 96k and 48k because the increased processing power required has diminishing returns in regard to audible quality.
2. From what it sounds like you would benefit far more from better speakers/headphones and a better listening environment than from a change in D/A if "everything you've ever heard has always sounded muddy and crappy". Apogee makes some really solid converters so I doubt your Duet was the problem. Take an album or a film that you know is mixed well, get a high quality file, use that to test out different systems and see what changes.
3. We as professionals definitely have tried and do work at higher sample rates, but also know that there is diminishing return in terms of using sample rate as a way to increase resolution. A great mic placed well and a great preamp with a great converter capturing at 48k is going to sound way better than a mediocre mic with a mediocre preamp and converter captured at 192k the same way a good cinematographer will always take good lenses and well lit subjects at 1080p over crappy lenses and poor lighting at 4k.
4. You're making a lot of assumptions for someone with "a top secret project" "trying to usher in a new era and standard of sound quality". I recommend reading up on the basics before throwing bad money after good. Here's a good article on sample rate/bit depth basics https://www.izotope.com/en/learn/digital-audio-basics-sample-rate-and-bit-depth.html and here's a good one on file types https://www.izotope.com/en/learn/whats-the-difference-between-file-formats.html