I've solved the obstacles to getting exFAT bootable under GNU+Linux! I never tried running EOSCard with Wine, as I wanted a native solution to get this working. I will explain what I found out for those who are curious, and provide attachments to the fixed files for those who want something quickly working.
Problem #1: make_bootable scripts have incorrect line breaks
The files on the Google Groups page are problematic and ideally should not be linked to in the official ML instruction PDF and wiki as they are. The make_bootable scripts are not executable on my systems (I tried on multiple distributions of GNU+Linux) because the endings of the lines are CRLF which stands for a Carriage Return character followed by a Line Feed character. This is the default newline notification for text files under DOS/Windows, but in Unix-based OSes (including GNU+Linux and Mac OS X), newlines are notified by only a Line Feed (LF) character, with no CR in sight. Bash was unable to execute the files as they exist on the Google Groups page because it needs all CRLF to be converted to LF in order to sanely determine where the line breaks are. It's tricky because in a normal text editor, you do not see the difference, but if you use for example the 'file' command on the bash scripts, you will see output similar to this:
make_bootable.sh: Bourne-Again shell script, ASCII text executable, with CRLF line terminators
This last part of the output of 'file' tells us why this script is not executable by default. To convert CRLF line breaks to LF ones, there is a utility called dos2unix (most likely available as a package of the same name in your distribution of choice) which does the job quickly and easily. After running this program on the make_bootable script, file now reports it as such:
make_bootable.sh: Bourne-Again shell script, ASCII text executable
With no mention of CRLF in sight. After doing this change, the script posted by 'arm.indy' on the Google Groups page became executable on my systems. Unfortunately, while the scripts seem to execute and exit with success, they caused my SDXC cards to not only be unbootable, but completely unmountable and unreadable on both my camera and PC. Debugging the mounting errors on my PC, I found the fault to lie with the exfat_sum program, which brings me to...
Problem #2: exfat_sum.c was written by a 32-bit OS user, for 32-bit OS users (won't work on 64-bit!)
After getting the make_bootable script working, I found out that the exfat_sum step was calculating the wrong checksum on my systems, which are all running 64-bit operating systems. The problem lies in the exfat_sum.c source code file, where there are 4 instances of "unsigned long". long numbers are 32 bits on a 32-bit OS, but they are 64 bits on a 64-bit OS, meaning for those of us on 64-bit OSes will have different (incorrect!) values calculated by the compiled exfat_sum program. To fix this, I changed every instance of "unsigned long" to "unsigned int" in the source, because int values are always 32 bits no matter what platform you are running. Changing these lines, recompiling, and running my fixed make_bootable.sh script finally produced a mountable, bootable exFAT filesystem.
I copied the ML directory and autoexec.bin file to the exFAT filesystem, and Magic Lantern was instantly working on my 128GB cards! Note that I had previously initialised my camera with a 32GB SDHC card with FAT32. I do not believe you can skip this step and still have a working SDXC/exFAT card with ML on it, even if you successfully make the exFAT filesystem bootable using the above methods (or other known working methods such as EOSCard utility on Windows).
If you are uninterested in duplicating the steps I gave, I have attached the fixed versions of the 2nd make_bootable.sh script and exfat_sum.c files in this post. I hope this information or files are useful to other *nix users down the line!