In addition, I have 16-bit WAV files made directly from raw, studio master tapes and want to burn to 16-bit CDs.
In researching, only speed is mentioned as an attribute - not the ultimate accuracy of the burn.
What design is most accurate?
Slot
Tray
Clam shell
There is absolutely no difference in their accuracy.
You have to realize, “accuracy” is one problem these burners do not have.
They either work or they don’t work.
In that case, the quality will depend on what software you use to convert the 24-bit FLAC to audio CD format. Once you've got the .wav file on your computer, it doesn't much matter what drive you use to burn it onto a CD. You won't be able to avoid some loss of quality.
See here.
All of the devices you listed contain the same drive hardware in a different enclosure. All DVD/CD drives write correct data to the media. Recordings can be bad on cheap media, which is not the fault of the recording mechanism.
All drives make errors, but they are negligible. On audio CD’s, the few errors a drive might make are inaudible.