Just as I had suspected, the new 16mhz crystals work great.
Getting a second Arduino running on the breadboard went smoothly. I wrote two programs, one that blinks an LED and sends a byte through the serial connection. The other program waits for serial data and blinks the LED when it receives a byte.
The setup worked flawlessly with a wire connecting the two Arduinos. The plan was to then swap the wire with the wireless module. Unfortunately, it doesn't work at the moment. I tried at 4800bps and 2400bps, but the receiver never gets any data. I don't know how to debug whether the transmitter isn't sending or the receiver isn't receiving. So that's the plan for next time.