So...
I bought my Mac Pro 1.1 like 2 years ago for very VERY low price. I used to pimp it up with dual X5365's, 16gb of RAM, SSD, hd5770 AND recently r9 270x. I also installed macOS 10.11 using tutorials on the web. Im very happy with that piece of hardware, but I think that we should TRY to give the 10.12 (or the new 10.13) a shot. I've come thru every page and every post that mentions why its impossible or very hard to do, and i think that the easiest solution will be sse4.1 emulator, running on lower level than kernel (i'm not very into smc, uefi and stuff like that on macs). But, i'm a developer and i know that its possible. I made a quick research on the sse4.1 iintruction set and found out very good informations:
"SSE4 does not introduce new data types, it uses data types defined in SSE and SSE2"
That makes it possible to write the code with less effort, SSE4.1 introduces 47 new instructions that can be also used as a mix of other instructions that are present in our wonderful mac pro's 2.1 cpus. I also found out a piece of software called "Intel Software Development Emulator" that brings the sse4.1 instructions to older cpus, but it works on different level that we need. It goes between software that need these instruction set and the kernel of os (idk if i understood it right). I havent looked deeper into it, but its available for download as source code (also for macos) and its propably possible for someone with big developer skills (not me ;c) to convert it to use on lower level, required to run osx newe than 10.11. Maybe I just make myself a hope and its impossible, but i really want to see sierra on these babies and i will help with that as much as i can.
Edit: Link for ISDE
https://software.intel.com/en-us/articles/intel-software-development-emulator