It would be helpful to know the wattage of the lightbar, but yes sounds like you arent charging the battery with the lightbar on.
The voltage regulator isnt going to help generate more power, it would just keep from burning out at higher generation from the stator. All the rectifier does is turn generated AC into DC with diodes. Those diodes have a maximum wattage rating, and if you exceed that (more amps or more volts) you can burn them out.
Bigger battery and/or plugging into the wall to recharge the batt are possible bandaid fixes, but dont address the core issues. I'm not aware of a bigger stator available. Easiest fix would be to buy a slightly lower wattage lightbar, and convert the headlights to LED. I've never seen any specs for what these generate, but typically stator based charging systems don't have a lot of extra power past running the vehicle lights and ECU. Maybe an extra 10 amps/120 watts.