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Lars - Thank you for your response. There are a variety of sign conventions possible. I usually consider all LHAs as positive or absolute values. Since LHAs come into calculations through the Cosine, the sign you pick doesn't matter much, as Cos(LHA) = Cos(-LHA). Pollux is east of Capella from their SHAs. It seems that the higher latitude solution is actually east of Pollux, as LHAC - (rather than +) LHAP is equal to the difference in SHAs.

I had thought that simultaneous transcendental equations involving Sine's and Cosine's didn't have analytic or closed solutions, but I may be wrong. I had made a table of latitudes and their associated LHACs and LHAP's, and then searched for latitudes where LHAC + LHAP, or LHA - LHAP equaled the difference in SHAs. This is basically solving the equations graphically.