Using the Arduino as a FTDI cable worked.
I was able to install the newer bootloader but only when using just the 3.3v Tx/Rx and the ground pins from the Smoothieboard to the Arduino. I powered the Smoothieboard via its USB port, and the Arduino through its USB port.
After installing the bootloader and disconnecting the Arduino, I reset, then saw my SD card mounted through the Smoothieboard. I dropped a config file onto the drive, reset the board, then tested my X and Y steppers. It took a bit of tuning in Pronterface, but I was able to eventually get them to run smoothly by adjusting the mm/min.
Now I'm curious - my stepper motor datasheet says they need 24v at 1.8A when driven as bipolar. Is 1.8A getting too close to the 2.0A max?
Also, I'm a bit new to working with steppers - should they get insanely hot? I have a Makerbot Replicator and have certainly never noticed the motors being as hot as the steppers I just tested on the Smoothieboard. I understand they use energy to maintain their position, but what I'm wondering is if someone can explain why they seem dangerously hot (too hot to touch within a minute or two of being idle).