It is known that the mean of the pi0 mass peak increases with pT.  Here's one thought I had, as well as a way to test the idea.  The following is focused on pi0's in the endcap, but also applies to the barrel.

We expect (define/require) prompt photons to not be part of a jet, but we expect that all of our pi0s are parts of jets.  We just don't see the jet to well because we only have the EEMC and not any tracking or hadronic calorimetry.  My thought is,  when we sum up the energy in the 9x9 block, centered at a given "seed" (high) tower, how much of this energy is due to the particle of interest (causing the high tower) and how much is due to the jet?  We'll call all towers above a certain threshold a "high" tower, providing that there is not another tower in the neighboring 8 towers with higher energy.

One thing to investigate is the energy flux near the tower vs. the energy flux of the tower.  By energy flux I mean the energy divided by the area, and area in meaningful units (cm² or m²) not in the units of eta*phi.  One could plot the total energy flux of 24 surrounding towers (not counting the high tower itself) as a function of the energy of the tower.  One could also plot the ratio of the energy flux of the high tower over the energy flux of the surrounding area, also as a function of the energy of the tower.   These plots could also be shown as a function of pT, assuming a single particle hit the center of the hit tower.

In the case of another high tower in the surrounding area of a high tower, one could still look at the ratio, but take energy flux of the two (or more) high towers over the energy flux of the unions of the surrounding towers.

The results would show how much the high towers stand up above the surrounding "noise," where part of the noise is due to the jet.  One could possibly use this scheme to subtract off the background energy (event by event) and see if it corrects the pT dependence of the pion mass.  Or if the ratio is relatively stable, an average subraction could be considered.  But if the background energy increases with pT, it is quite likely that this is the cause of the shift.