I think I lurched into a way to get an approximate answer based on the information about barrel velocities in my post above.
You can get an exponential velocity profile by using the data that the velocity is 98% of the muzzle velocity at 90% of the barrel travel. I assume that the travel is 61 ft., the other 5.5 ft being taken up by the propellant charge.
That velocity as a function is distance is:
v(d) = 2615(1 - e[sup]-0.06387d[/sup])
Then the distance traveled can be broken up into 5 ft long segments. Make the assumption that the velocity varies linearly during the segment. The time to travel each segment is the disance travelled divided by the average velocity during the segment. Compute these times, add them all up and we have the approximate time in the barrel.
My answer is about 38 milliseconds.