Below is the predicted lunar transit path generated by my WorldView program (Eastern Daylight Time = -4.0 from UTC).  The SVPOST mark uses a TLE from spaceflight.nasa.gov/realdata/sightings/SSapplications/Post/JavaSSOP/orbit/ISS/SVPOST.html :

1 25544U 98067A   03156.55560875  .00041100  00000-0  34010-3 0  9038
2 25544  51.6317  78.6891 0006584 216.8025 143.2679 15.59228434 19196

while the OIG marks (which are basically in agreement, but about 2/3 second ahead) use a TLE from the Orbital Information Group oig1.gsfc.nasa.gov : 

1 25544U 98067A   03156.49151735  .00014188  00000-0  17667-3 0   836
2 25544  51.6320  79.0095 0006663 217.9964 142.1082 15.59236303259188

I entered latitude = 34.9357 / longitude = -82.0738 (corresponding to SVPOST 15:40:57) as my site location at www.calsky.com, which tells me that it computes the centerline as being .47 km = .29 mi to the southeast of my track.  A possible source of the discrepancy is that I use the WGS '72 geodetic model, while CalSKY uses WGS '84 (it's unclear what Microsoft Streets & Trips uses!).

I'd be interested in seeing comparison predictions by SkyMap, STK, The Sky, etc.

Time Object Event
  Observer Site User Site, United States  
Geographic: Lon: 277d55m34.3s  Lat: +34d56m08.5s  Alt: 205m
WGS84: Lon: 277d55m34.3s  Lat: +34d56m08.5s  Alt: 205m
All times in EST or EDT (during summer)
15h40m56.9s ISSISS Crosses the disk of Moon. Separation:0.05d
Angular Velocity:54.6'/s.  Transit duration: 0.56s
Angular diameter: 9.5"  cylindrical, 20.0m x 10.0m
Direction towards center line: 0.47km, az:128.8d SE
az: 105.3d ESE  h:  53.9    dist: 483.6km mag=-0.5m