Well, it seems that in my troubleshooting process, I never once had the software for the Gameboy Cartridge Flasher up without the actual device plugged in. However, I was in a hurry to run a few more tests and had my cable connected to the computer and not the device, and strangely enough, it found the Cartridge Programmer!
Wait a minute... That can't be right... I don't have an IR receiver on the GBCF!
It turns out that my cable was not a straight through serial cable, so I am now finally just making my own DB-9F to DB-9F null modem cable and returning the $11 RipoffShack null modem adapter.