I have been using the IMU simulation
One thing that became clear quickly was that neutrons are not negligible. We could afford to ignore previous crossings in Run I, but the neutrons from a previous crossing will still be hanging around for later crossings in Run II, and the raw scintillator rates become roughly double what you'd expect from ordinary prompt backgrounds.
For part of Run I we connected 9 of our West rear scintillators to TDC channels, and looked at the timing of hits in the scintillator. I used the predictions for the inter-toroid counters as a model for the neutron rates for the rear scintillator in the FMU in Run I. I didn't put in the low beta quads, which I expect to have a substantial effect, nor can I use MARS results for beam-line junk. The distributions have different shapes, but aren't actually inconsistent because the data occupancies are over 40 times the rate I predict. I'd say that GEANT does not overestimate the background.