The power board prototypes arrived today. I built one out and connected it up to the oven. It works perfectly.
I fed it with a 5 volt power supply and a 200 ohm resistor and it turned the elements on and off like a perfect light switch. I left it on long enough for the elements to glow red hot and then quickly unplugged everything and checked the triac heat sinks and they were cold. I've now got no doubts at all that it's going to work. Next step will be to build it into the oven and button everything up.
Anyone who wants to follow along should now feel confident in getting their own power board from OSHPark. You can find the design here. It's $22.40 for 3 copies of the board, but I'll sell them in single quantities in my store.
The power board is designed to switch up to 8 amps per channel (this is based on the width of the current carrying traces on the board and the heat capacity of the heat sink). As long as you can split the load in half, you should have no trouble switching 1500 watts.
To use it, you bolt a QD male terminal onto each of the 3 large holes in the middle of the board. The centered one connects to the hot lead of the AC input, and the other two go to the load - in this case each of the two heating elements in the oven.
The 3 terminal block at the end of the board has a common cathode pin and an anode pin for each of the two channels. You must use current limiting resistors on each anode line. The LED in the opto-isolators is rated for 30 mA with a forward voltage drop of 1.5 volts. Make sure you do not exceed the opto-isolator's maximum current rating of 50 mA. You should have no trouble driving them with an AVR digital pin directly with just a current limiting resistor in series.