Rip all the wiring out and start from scratch.
(Less expensive than replacing your Jeep)
Re-do the whole lighting circuit using larger wiring.
As far as "Off road lights versus driving lights...
An H3 Halogen bulb is just that!
There are no differences in H3 driving light bulbs or H3 off road light bulbs!
The differences lie in the design on the lamp unit itself. And weather it, "The lamp unit has a "Heat sink" incorporated in the design." Which most do not!
For example, look at "Track lighting" in a home or business. They too use H3 Halogen light bulbs!
Yes, some are line voltage (115 volts), others are powered via a 6 or 12 volt transformer!
I know for a fact that the ones I have installed in my living room come from an automotive parts distributor!
My living room does not have 30 plus miles per hour airflow sailing past my track lighting to keep them cool!
And they work without incident night after night for many a year!
Check the grounding of the light circuit.
It's been my experiance that most electrical problems stem from a dodgy ground!