You could create a boost transformer with a 100va or so (I doubt you need any more than that) 120/240 to 24 vac control transformer. You just connect the secondary in series with the primary and run it as an autotransformer. If it had dual 120 primaries, you put all three coils in series and power it with 120 for an output of 120+120+24=264 volts. It will have to be phased correctly otherwise it will buck rather than boost. Trial and error will get you there, just test unloaded with a voltmeter. That’s about the best you can do with commonly available parts.
Hopefully you can get a transformer for really cheap or borrow one to test because it probably will not make much of a diffference in the burn. Ballasts are a poor choice since they are designed to limit current. A byproduct of that behavior is that the output voltage drops off in order to maintain a constant current. The only way to increase the voltage is to increase the resistance of the wood - which means dry it. This the opposite of what you really want. Translation? Ballasts don’t work for the purpose and I don’t think jacking the input voltage up is going to make any difference. The moisture content of the wood is going to determine the voltage.
A repurposed transformer from an old, big microwave (modern ovens don’t have transformers) is a better choice since it’s a straight step up transformer without the inherent current limiting. If you overload it, yes the voltage will drop when the core reaches saturation but you don’t want to let that happen since that will let the smoke out.
Put big Powerstat/Variac (at least 6 but 10 amps ideally) on the input to control the voltage/power and you’ll have voltage to burn 