j0hnsmith I wanted to ask and point out a few things on your method.
I think when you install the "mw3 patch v103 (zombiekillah)," the reason it gives you an error is probably because it is overwriting all the other files and kicking it back down to 1.03. Have you tried it without it and what error did it give you? The original game i have is version 1.0 and so I just installed 1.19 and onwards. I did not install the 1.03 patch and did not have a problem, I believe that was mainly to spoof and bypass the requirement to patch when the game actually booted and you tried to find a server, back in the day.
Also if you are manually extracting each package on your computer using ps3tools, are you merging the folders from 1.23-->1.22-->bundle. When you are doing it on the computer, you have to be sure and merge the folders and only overwrite the files you are updating. I am not sure what OS you are using but I have often had the problem that when i was trying to merge two folders together, it would replace the entire folder and would not keep the old files. And so I would have a "merged" folder with only the new files on it and none of the old ones.. Have you tried just simply putting those packages on a USB and using the XMB to install them in sequential order?
Lastly for the final step when you are copying over the eboot fix. There is an integrated file manager with multi-man called mmOS. So if you copy over the folder with the eboot fix onto your USB thumb drive you can copy and paste it over to the appropriate directory from there, onto your dev_hdd0/game/BLUS or whatever version you got. If you need a deeper explanation, let me know and I will write out exact file names and a step by step process lol.