Take a look at this very brief (3 pages) paper. The author proposes yet another possible way to avoid the SU(2) → SO(3) problem by replacing SU(2) with the supergroup Osp(1|2). In this case, the immirzi parameter is twice the usual non-supersymmetric value, one consequence of which is that, effectively, only integer spins contribute to area.

http://xxx.lanl.gov/abs/gr-qc/0309018
Btw, I found equation (20) - particularly it's left-hand side - oddly moving, though I couldn't quite put my finger on why.