Does the burner say how much current it demands? Like on the back? That is a needed parameter if you are going to build a regulator.
If you are going to build a regulator though, I'd just build a whole PSU. I don't really see the point of battery powered regulator in that case.
The current draw isn't likely to be constant for a burner. You can use a voltage divider to drop the voltage (with resistors and/or caps). You can always try with 13.8v. I'd guess it'd be ok, but don't know for sure.
If you plan to use this as a transport, I think SLA's aren't going to be worth the effort, but that is my guess.