Hey Brian,
There are so many different places in the chain that you describe, where it could go wrong.
When doing a “3840×2160 mp4 with custom data rate of 100,000 kpbs, which is the max, with multi-pass checked.” you are stretching the capabilities of most kit, including high-end 4K televisions.
I would suggest that you instead of using MP4 which is IMHO not a stable format, do a DCP out, take that to your local Digital Cinema and screen it in private. That way you’ll get to experience it the way that you want your audience to do it.
The other route is to get a 4K monitor calibrated for grading – Eizo is a good place to start.
But do keep in mind that Apple likes to mess with your file imports, so they will always playback in time line.
Uploading a MP4 file to a festival or similar, if they are using AWS or similar, there is every chance that they will re-encode your MP4. Just because those using the service might have “ticked” the wrong box somewhere.
And, then there is your MacBook Pro, which is hardware that I am NOT a specialist on. But depending on the HDMI output, cable, or just the TV, they will all conspire to make your piece of art look rubbish – in short, there is every chance in your chain to the TV that the signal is automatically down-converted to HD, then up-converted back to 4K, just because one part of that chain can not work with 4K.
Do consider playing back a 50 Mbps file in ProRes 4K from the Mac onto your TV, and see whether that changes the image quality?
But best way forward is to view it where it is meant to be viewed, in a file format that works for the distribution chain. Everything else, will ruin your day, as it will never be a good “blown up” as on your smaller MacBook Pro screen.
Hope that this helps?
Atb
Mads