I've done it! I have created a v1.0-compatible retail 5101 BIOS!!! It is even compatible with v1.0 EEPROMS!
I have been testing it for about 3 hours now with MANY games and applications, and everything seems to be functioning perfectly! And it is 100% compatible with ALL NKPatcher v10 functionality, including VGA/Force480p!
And on top of that, my v1.0 XBOX now has the 'graphical detail' in games that the v1.1-1.6 XBOXes have. Example: In some games like Halo 2, there are areas where the graphics will either flicker or glitch, or will simply not fully show up, even when up close. This is a strange phenomenon that many v1.0 owners have noticed, and v1.1-1.6 XBOXes do not have this problem. The reason it happens is because the GPU code in 3944/4034 BIOSes was in it's 'infancy' at the time they were built, and therefore the GPU code had a few issues. These issues were obviously resolved in later BIOSes, specifically 5101 and higher. Now that I am using a 5101 BIOS on my v1.0, those issues are non-existant.

NOTE: 5101 was the highest kernel I could get to boot on my v1.0 XBOX, the rest would either COMA or FRAG. In order to use the 5101 BIOS, I had to extract the 5101 kernel 'xboxkrnl.img' from an original v1.1 5101 BIOS, and pack it into a new BIOS file using the '2bl.img' and 'remainder.img' from a 4034 BIOS. So, the structure of my v1.0 5101 BIOS is as follows:
2bl.img - Bootloader from 4034 BIOS
remainder.img - Remainder from 4034 BIOS
xboxkrnl.img - 5101 Kernel from 5101 BIOS
*NOTE: I did not include the 'fbl.img' file from the original 5101 BIOS because it is not necessary on v1.0 XBOXes. Also note that I have made absolutely no changes to the 5101 kernel, it is still completely original.
Therefore, the 5101 kernel is completely compatible with v1.0 XBOXes, it was simply the remainder/2bl/fbl files in the original v1.1 5101 BIOS that were not compatible.
Tools used to do this:
PBL Lite - Used to test functionality of BFM 5101-5838 retail BIOSes on v1.0 XBOX. (5101 was the only one that was compatible.)
XBtool - Used to create BFM retail BIOSes, and also used to create flashable/packed retail BIOSes.
Raincoat v0.7 - Used to flash test BIOSes onto the 3rd bank of my TSOP, and also to flash the 'final' compatible 5101 BIOS. (Lots of tedious testing...)
I will be releasing my v1.0 5101 BIOS, hereby known as 'Frosty's v1.0 5101' to the 'usual places' for those who are interested.