I am posting this mostly for the benefit of others. There are plenty of threads all over the place on the issue, but I was unable to find a good answer anywhere else and ultimately found a solution on my own.
In my project we wish use the ARM compiler for release builds, but due to the cost, we would like to avoid using it for development work. We are using the GCC compiler as an alternative for development since the code and assembly are more compatible to the ARM compiler than the between the ARM compiler and the TI LTS compiler.
When using the GNU tools available in TI Code Composer Studio or using the ARM-provided GCC compiler, I found that you could build your source code as big endian, but the program would not build since all of the built-in libraries support only little-endian systems.
I did a lot of searching online without much help. I also tried to build a cross-compiler from several versions of GCC source. I was able to build a native GCC compiler, but make always crashed when trying to build a cross-compiler for ARM.
Ultimately, I found that Linaro provides the binaries needed for building code for a big-endian system on their website here:
https://releases.linaro.org/components/toolchain/binaries/
You will find the toolchain supporting ARM big endian as armeb-eabi. At the time of this post, I was able to find a compiler for GCC 7.5.0, which supports C11, C99 and C89 in case you are programming in C. This can be easily added to TI CCS by unzipping the files and adding the folder as a compiler search path in preferences.
I hope that someone can save some time by reading this.