This is the problem with floaters and step downs. Floaters must have that expansion space. So if you glue and nail the stair nosing, you need to allow for expansion where the flooring meets the nosing. With the flooring you're using, I don't know right off what that expansion requirement is. Consult the manufacturer. But do leave that expansion. Then cover the gap with whatever you want. A piece of matching wood 5/16" thick and about 1&1/2 wide, beveled on the sides, could be used. Or that T-molding. Problem is, then you have that little bump right there at the top of the stairs. For that reason alone, I'd go with a direct glue or nail down, IMO.
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