I've tried hitting the RESET button the STK500 both before and after starting the 2nd download and it doesn't appear to make any difference.
That's a little confusing to me. Does that mean you are using the STK500 to load the second sketch, after loading the first sketch using the Arduino IDE?
The Arduino IDE uses the serial USB link to upload sketches with the active bootloader running on the board talking to AVRDUDE. Loading the bootloader into the AVR chip with the STK500 is a one time operation, after that normal uploading is done via the serial link, not via a STK500. If you use a STK500 to load a sketch it will overwrite the bootloader.
I may just not be understanding your last statement.
1. Program bootloader With a hardware STK500 programmer, correct?
2. Download "blink" sketch via Aruino IDE Using normal USB serial connection?
3. Attempt to download new sketch fails Using USB serial connection or a hardware STK500 programmer?
, first downloaded sketch is undisturbed and still running.