Figure 1 shows a plot of the area under the unexpected peak in non-adjacent-tower candidates at m=.3 vs. eta and phi.  While some hot spots are visible, they just aren't big enough to account for a sizable percentage of the 12000 entries in this plot.  Also, while some do match up with Mike's list of lukewarm towers, many do not.

Figure 1: Eta-phi distribution of candidates in the peak at .3

On the simulation side, the attached pdf shows the true photon z-reconstructed photon z (from linear energy weighting of the strips in the cluster) in eta bins.  Note the 1 cm shift, which has the same sign as the z value of the photon.