UPDATE:
JPLinearFitAveragedWithHTDistributionFit-Rings.ps shows the ring-by-ring plots used to determine the final ring mean E/p value.
The JP triggers are broken into 0.5 GeV momentum slices which are then fit with a Gaussian+exponential to determine a mean E/p value for the momentum slice. Then the momentum slices are plotted (black crosses on top of the 2D histogram), and then fit with a constant (giving each bin equal weight). The value of the constant fit is used as the JP mean E/p.
The HT tracks have a more stable E/p value, so all the tracks between 2-3 GeV are used to create a E/p distribution which is then fit with a Gaussian+exponential, which is used to determine the mean E/p value for the BHT2 trigger.
These two mean E/p values are averaged together to get a final E/p value for the ring.

PreliminaryBEMCGainsUpdate_v2.pdf contains a couple slides showing the MIP peak distributions for previous calibrations as well as plots showing the change in individual towers. I looked into the HV changes, and it appears there was only one change that occurred between 2012 and 2015 and that was on February 3, 2015. I was not able to find documentation showing the direction of the change.

UPDATE 2:
The files labeled RingXFiducialCut.pdf show the E/p vs p distribution for various cuts on the track-tower radius at the surface of the tower (the same radius used for the MC correction).
I've included the four outermost rings, as well as one central rapidity ring for comparison.

UPDATE 3:
HTOuterRings.png shows the E/p value in each ring with and without including BHT2 in the outermost rings.

UPDATE 4: 
ExtrapolationOfPenultimateRings.png shows the linear fit of rings 3-6 and 35-38, which is used to determine what the trend of the difference between BHT2 and JP means should be in the outermost rings.
DiffExtrapolatedvsExcluded.png shows the gain difference between the gains calculated where BHT2 is excluded in ring 1,2,39,&40, and where the BHT2 difference from the JP mean is extrapolated into those rings.