After draining the carbs and playing around with the choke a bit, I was able to get it to start. However, it runs for about a minute before bogging down and dying. While running, I could hear the sound of air escaping, and smoke was coming out around the rear cylinder header. Looking at the exhaust flange (the piece that presses the exhaust header to the cylinder), it looked like it was bent pretty bad.
I removed the spark plug cap from the rear cylinder spark plug, so that it would only ignite on the front cylinder. It then idled pretty well, as far as I can tell the idle was very consistent.
I tried fixing the exhaust leak by using some high temperature RTV gasket maker/sealant, which did help, but it wasn’t perfect (plus that stuff makes a mess). It idled better afterward. Later, I just replaced the exhaust flange studs (the screws on the cylinder which goes through the flange, with nuts on the end to press the flange against the cylinder).