I have located some engineered sliced strip flooring (3 ply, 5/16", 3" wide, 36" standard length) that specifies the glue down method.

While I haven't ruled out a glue down installation, my question is - why can't you install this as a floating floor?

The flooring - while not a locking type - has the tongue and grove construction (I think that is the correct terminology for the male and female sides). Why can't I just purchase the correct type of glue for floating jobs and apply a bead in each of the grooves?

I understand this may void the warranty, etc, but I'm having a hard time understanding why the manufacturer didn't allow for both installation methods. Am I missing something here?

While it MAY work, it very well may not. Personally, I wouldn't float anything under 5" wide. If the manufacturer did not recommend for floating, they have a reason. Probably the T&G is not big enough, strong enough, tight enough, etc.

Sloppy fast milled T&G. It will eventually separate if you try and T&G glue it.