The power board is rated for 8 amps per channel. That limitation is a factor of two things - the traces on the power board that connect the oven's innards to the traics, and the ability of the triacs and heat sinks to dissipate heat. According to the data sheet of the BTA-20 triac, at 8 amps, it generates 10 watts of thermal power. The case-to-mounting-tab is rated at 2.1 °C/W. The heatsink I chose has a rating of 5 °C/W. So 7.1 * 10 is 71 °C temperature rise at rated power. The maximum junction temperature is 125 °C, so that means that the maximum ambient temperature for the power board is 50 °C, or 122 °F. I stuck a thermometer in one of the vents and ran a cycle and the temperature near the heatsinks never rose above 100, let alone above 122. That's a bit of a surprise, given that that chamber is right next to an uninsulated metal box being heated internally to 225 °C. Credit the ventilation, I guess. Undoubtedly it's so liberally ventilated to insure that the original user controls remain cool to the touch during use.
As for the traces on the power board, they're a minimum of .1 inches wide at the thinnest point, and they're on both sides of the board. OSH Park's boards use 1 oz copper. Since we're using both sides, that's either an equivalent of 2 oz copper or .2 inches wide, take your pick. Plug those into this calculator and you get that a maximum current of 8 amps requires 104 mils of trace width with 2 oz copper on external (air facing) traces. Most of the current-bearing traces are wider than that, but it does become quite narrow right where the triac pins are.
The boards are $7.50 each from OSH Park. The BOM from DigiKey is just under $10, plus shipping and tax. I took a look at DigiKey's catalog, and there are SSRs they stock that are competitive with this design, but they don't blow it away in either price or performance, and the best option I found would have been more difficult to deal with from a thermal perspective. Standalone SSRs, like those I've seen people use on the Internet, are many times more expensive.
The controller boards are $4 each from OSH Park. The BOM is $12. You also need an OpenEVSE RGB display backpack, which sells for $35. And the oven was $40. So, in short, the whole thing was around $115.