I looked into updating the existing libraries for FAT32 support at one time, but didn't have a sponsor for the work. Based on the existing APIs including integration with buffers in non-volatile BBRAM and logical-to-physical sector mapping, I thought it would be easiest to update the current library's code rather than try to port in a third-party library.
One hassle with porting is the need to update pointer definitions to work with "far" pointers.
But the library you linked looked promising, and I believe the MicroPython project made use of it for SD card support on the Pyboard.
The updated Dynamic C libraries at least work with newer SDHC cards, and the limitation of four 2GB FAT16 partitions on a device is an inconvenience but not a show-stopper in most cases.