I'm sure this is "possible", but my question is "Is it worth my time and effort?" The manufacturer will sell me a new board for $100, but that seems expensive for such a simple board, especially when I already have all the components. Also this would be a good learning experience for me.
The item in question is a 120v 1,500 watt infrared heater that looks similar to this one, except the one I have has a cord hanging down with a temperature sensor at the end:

This is a picture of the front PCB:

And this is the back (obviously it's much more difficult when the back is covered like this):

The piece missing at the top is a burned out TRIAC (CQ3P-25D). I already have a replacement for that piece. I was planning on just popping in the new TRIAC, but unfortunately it looks like some of the traces got burned out on the back of the board as well, so that's why I'm interested in just re-making the entire circuit if possible.
Items on the board:
-1 large (looks like 2 or 3 watt) 10K resistor.
-4 smaller resistors, measured at 2.7K, 2.1K, 87K, and 42K
-1 analog potentiometer
-1 100uF 64V capacitor
-1 1uF 50V capacitor
-1 CQ3P-25D TRIAC (datasheet:
http://pdf.datasheetcatalog.com/datasheet2/8/0ux48tck2xw8d4qyo4eychws54cy.pdf)
-1 V14241U “ZNR” Transient/Surge Absorbers (datasheet:
https://industrial.panasonic.com/cdbs/www-data/pdf/AWA0000/AWA0000CE2.pdf)
-1 CA3059 "Zero Voltage Switch" (datasheet:
http://www.onsemi.com/pub_link/Collateral/CA3059-D.PDF)
The datasheet for the zero voltage switch contains some example circuit diagrams, like the one below:

The 3 wires coming out of the top of the board are Line, Neutral, and Output to the heating element.
The 2 blue wires coming out of the bottom are for the temperature sensor.
The device changes the heat levels by changing the frequency that it's turned fully on and off. If the pot is set to the highest setting then the heater might stay on constantly, but if you put it in the middle, it'll flash on and off a few times a second, depending on the temperature of the sensor at the end of the cable.
Thanks for any advice!