Using an Arduino to talk to another Arduino's bootloader

I've recently been experimenting with the Sparkfun MicroView board (essentially an Arduino with an OLED screen and no onboard USB programmer), and keep running into memory limitations (the graphics libraries for MicroView alone take up 38% of available program space). To get around that, I wanted to use a second Arduino with an SD shield to provide a sort of on-demand reprogramming by pushing an image via the MicroView's bootloader.

I've been trying to get the bootloader on the MicroView to respond to the other Arduino. The test sequence is as follows:

  1. Pull the RST pin on the MicroView low for a bit. (I'm using 100ms, just to be safe)
  2. Immediately upon bringing RST high, send a command to the bootloader. (Google tells me the bootloader is Optiboot, which supports a subset of the STK500 serial protocol. I'm sending STK_READ_SIGN, character sequence 0x75 0x20 ["u "], at 19200 baud)
  3. Bootloader will return DC4 (0x14), followed by a three-byte signature, followed by a linefeed (0x10).

The bootloader isn't giving me a response, and changing baud rates (I've thus far tried 9600, 19200, and 115200) doesn't seem to help.

Immediately upon bringing RST high, send a command to the bootloader.

"Immediately" might be too soon. The chip needs to reset, and perhaps blink the startup LED a couple of times.
Microview docs say that it appears as an Uno, which means optiboot at 115200bps.
Are you sure you don't have RX connected to RX and TX to TX, instead of crossed over? That's a pretty common mistake when connecting the serial ports of multiple AVR chips.