I spoke with J&R about using Liquid Nails, and they were pretty adamant about not using it, since it dries hard. They said that you need an adhesive that dries flexible, as our trailers flex a ton. I also stopped by my local trailer store to ask what they use in their trailers, and they showed me their gallon sized can of standard Contact Cement, which dries soft and adheres to foam, etc.
My father-in-law used to lay carpet, and said that Contact Cement should work excellent, so that was my plan. I'm not familiar with Henry 663, but will look into it.
I know that they make tons of different types of Liquid Nails, so maybe you found one that dries soft and will work well.
I am also going to do this, as I have channels already cut in my foam, where there was like 1/4 or 5/16 plywood already, that was the anchor for the cabinets (it was totally rotted in mine, hence the reason my cabinet was falling from the roof). I was thinking of using OSB instead of plywood, as I thought it might be resistant to water more than plywood... any thoughts?