What are the special parahoric subgroups in unitary groups?

There's an explicit description of maximal compact subgroups of all unitary groups over local fields (not necessarily quasi-split) in section 3 of this paper:

Gan, Hanke, and Yu, "On an exact mass formula of Shimura" , Duke Math Journal 107(1) (2001).

This doesn't quite answer your more specific question, since it's not immediately clear to me whether or not their maximal compacts are larger than the ones you consider; but it should be a feasible computation.