> segmented memory is out in Protected Mode (nearly the totality of remaining 16-bit code).

No, segmented memory is exactly what you can get working. You set up the segments via the LDT, which is still supported even in 64-bit mode; this is how Wine is able to execute Win16 code on 64-bit Linux. (Reading Wine code is how I figured out how to execute 16-bit code from 64-bit code in the first place!)

What doesn't work, if my memory serves me correctly, is all the call gate and task gate stuff. Which is effectively building blocks for an OS kernel that everyone tossed out in the early 90s and instead went with kernel-mode and user-mode with the syscalls (first software interrupts and then the actual syscall instruction in x86-64). You don't need any of that stuff to run most 16-bit code, you just need to emulate the standard Windows DLLs like kernel, ntdll, and user.