Dumping firmware/software...and/or reflashing??

mikedehaan:
I hooked up the Arduino as an ISP and deployed a new version of blink and it worked.

Excellent.

The Arduino API refers to pins differently than I would have expected,

Should be top-left to top-right in a U-shape around the processor. That's how the pins on the Uno (ATmega328 based boards) are numbered.

One problem I still have is, the delay method seems to be running slow.

The program is compiled for 8 MHz and the processor is configured to run at 1 MHz. I suggest using this core...
http://code.google.com/p/arduino-tiny/

I added two ATtiny44 entries for you. Use this download...
http://code.google.com/p/arduino-tiny/downloads/detail?name=arduino-tiny-0100-0013.zip

Start with the ATtiny44 @ 1 MHz (internal oscillator; BOD disabled) board entry. After re-uploading, your program should blink correctly (±10%).

When you are comfortable everything is working correctly, select ATtiny44 @ 8 MHz (internal oscillator; BOD disabled) then execute Tools / Burn Bootloader. That will change the fuses (reconfigure the processor) to run at 8 MHz. Even though the processor is running 8x faster, after re-uploading, your program should still blink correctly (±10%).

Running at 1 MHz is a great choice for battery power. Running at 8 MHz is a great choice if you need the extra horsepower.

Thank you so much for your help by the way. I sincerely appreciate it.

You are welcome.