Actually, there is a factor 2 to take into accunt in the definition of the decay time we used, that is P = P0*exp(-2*t/tau)

(see https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-24-30114 )

So the decay time from the "hand cutting" fit should be:  2/tau = 3149 => tau = 0.6 ms.  Anyway, since I used this definition also for computing the filter cavity decay time (about 2.7ms) if I'm not wrong we have a factor 5 of difference between the two, in any case.