There are a lot factors you may not have match to each others. Your elevation above sea level may not be the same. Temperature and atmosphere refraction could add some difference. Calculating the light speed from Moon to location is close to a second of time. What data for calculation did NASA used for web base calculation. What size of the Moon did NASA used for calculation, width in arcseconds from you location or was it geocenter. These are too many unknowns to pinpoint the difference.

Denis

So I am chasing down an anomaly of the timing...

I was at
        37.06769 -88.10091
which is down to a 1.112 meter