I have a 30 LED 1157 taillight bulb. It's been in there for years. Don't remember how long and no problems.
The flat panel lights like described above from Custom Dynamics or Radiantz are good. I did not have luck with those little bulb replacements that have 10 or 12 leds in, in the same round shape as a bulb... those were cheap and gave off less light than a standard bulb. In daylight it was not bright enough at all. A larger panel is needed. The one in my tail light is from Custom Dynamics I believe, and works great.
Technology might have changed in the last few years tho..... but when those little LEDs didn't work our for me, I used halogen bulbs... much brighter. As for taking the load off the trailer.... hope you find some good LED's.... might want to check what the truckers use.