EPR is equal to the ratio of stagnation pressure at the turbine nozzle to the stagnation pressure at the compressor inlet.
Considering the compressor inlet. The dynamic pressure will go up as the aircraft accelerates but the static pressure will go down so the stagnation pressure remains constant here. However, the mass flow of air going through the engine will surely increase?? which will produce more thrust and therefore the pressures in the turbine must surely change??! So thinking outloud, I would expect the EPR to increase.
Looking forward to the feedback.