If it were me, I would take the LHT however I suggest you spend some time prior to the ride on both bikes, covering the same number of miles and see which one is more comfortable, I would do at least two days back to back of long miles on similar roads using your road bike to see what your body feels like the next day. Of course I am a comfort over speed rider any day and what I love about my steel bike is that ability to ride many many miles day after day without discomfort.
Sounds like a fun ride