I had problems with the first round of LED bulbs. What I found out is that they were rated for 12 volts. When the charger is running the system has more than 12 volts. I found bulbs that had a voltage range, I think something like 8 to 16 volts. These worked fine.
In your case it's also possible that the charger/converter could be an issue as the original unit introduces unfiltered DC current. That might be an issue with LED's.
I would make it a high priority to install a modern charger/converter. I used a Progressive Dynamics PD4645. Not crazy money, relatively easy to install, decent charge profiles(though not the best*) and assembled in the USA. The battery in my RT when I sold it was a group 29DC from Wally World, the Maxx version. After 2.5 years of use it was still performing well using the PD4645 and solar, boondocking about 4 months per year.
*The best($$$) chargers entail using tail current for charging control.
2000 Roadtrek Chevy 200 Versatile(sold)
'98 Safari Trek 2480
'15 Kawasaki Versys650LT
Perfection is a fantasy, though improvement is possible(Wifey).