Thanks for the advice, folks. The 'someone put an inappropriately hot bulb in the fixture' theory seems most reasonable. So, I've reinstalled the fixture as-is, covering the burned spot, and will replace all the bulbs with LEDs when I move the trailer out of the storage yard and have access to shore power. (The batteries are currently dead.)
For what it's worth, I pulled the bulbs out of the kitchen and dinette fixtures, and here's how they were labeled:
There was one of each bulb type in each fixture. One of these bulbs isn't necessarily the culprit; an extra-hot bulb could have been installed at any point in the trailer's life and then replaced with the correct bulb.
Here's a good thread explaining the difference between 1141 and 1156 bulbs:
1141 vs 1156 bulb....what's the difference?
Both the 1156 and the 1141 are Single eliminate bulbs using a BA15s single contact base. The glass envelope is a S8 on both. So they are physical the same size and would use the same electrical socket.
The difference is in the element. The 1156 is a 12v 2.1 amp 26.9 watts unit with 1200 hrs life. While the 1141 is 12v, 1.44amp and 18.4 watts with 500 hrs life. The 1156 produces 32 candle power while the 1141 produces 21.
The 1156 will produce more heat than the 1141 and that will require a slightly different design for a mounting fixture/lens cover/shade. Said a littel differently the 1156 in a 1141 housing may melt the lens cover/shade.
As to the use of an LED in a mount designed for either bulb I doubt that any problem from heat would be encountered using either. The LED for the 1156 would have more lumen's than one designed for the 1141.
It comes down to what is the requirements in lumen's for the application.
The LED replacement bulbs I can find on Amazon seem interchangeable with either 1141 and 1156 bulbs, and use model 5050 LED squares, which output 16-22 lumens each. These common replacement bulbs ($1.22/ea) have 15 LEDs per bulb, meaning a light output of 240-330 lumens:
Amazon.com: YITAMOTOR 20 X 1156 BA15S 18-SMD RV Camper Warm White LED Light Bulbs Tail Backup 1141 1003: Automotive
And these are 450 lumens, though quite a bit more expensive ($6.44/bulb; dropping into the $5 range in quantity):
Amazon.com: GRV BA15S 1156 1141 LED bulb 126*3014 SMD AC/DC 11-28V 4W High Bright Warm White Pack of 2: Automotive
So, I think I'll use the 240-330 lumen bulbs for most of my fixtures, and upgrade to the 450-lumen bulbs where I need more light.
Please let me know if you have different advice. Thanks!