I started a thread in strings over this, and the two most common asnwers to "tame the highs, add some warmth/mids" were DR Sunbeams, and LaBella SuperAlloy; so I may give those a shot after gigging the DA once or twice.
I would second the notion of the SuperAlloy set. I am using a set of Everly B-52's on my Super J/P which is bright by nature. I'm liking the combination. The only other time I used this type of string formula was on the Dark Starred LeCompte. It was much darker by nature, as you know, and was not a good combo...