I did some research, here are some details: The basic problem of dumping cartridges is that you'll somehow need to start the cartridge dumping program (CSAVE-Misc-02.zip), and that would normally require a different cartridge (i.e. Editor/Assembler) to be plugged in. This is because the TI-99/4A has no built-in way to run machine language programs, i.e. TI BASIC is basically a sandbox and you'll need a cartridge to escape it.
One way to circumvent this limitation is a hardware cartridge switcher - A device that accepts two cartridges and allows you to switch from one to the other while the system is running. That way, you can run Editor/Assembler, use it to run the cartridge dumper from floppy and then switch to the cartridge you want to dump.
Another way is to use a disk controller or disk emulation system that has a machine language loading program in its ROM. This will work with CorComp disk controllers and Horizon RAM Disks, which require the Peripheral Expansion Box (PEB), or with a TIPI, which is available in two different sideport versions as well as a PEB version.
I have a couple of TIPI boards that I can pass on, if needed.