Ah, Kornucopia. Unfortunately I never had access to it but from what I read it seems to be a valuable addon with a lot of useful functions.
I guess you followed in your sheet this article http://www.ptc.com/appserver/wcms/resourcecenter/mathcad.jsp?im_dbkey=135085 and I think it would be a good idea to replace my derivation routine for discrete data (diff()) with the appropriate Kornucopia routine, probably followed by some filtering As shown in the aforementioned artice). I am in no way convinced that my derivation routine will cope with outliers in all cases and so it may happen that the absolute minimum is not at the position you are searching for. In fact my first derivative routine (a simple deltay/deltax) suffered from that problem somewhere at t=9.5, where two datapoints are very close together. I was able to fix this by smoothing the second derivative using medsmooth() with a window of 3, but window=5 would smooth out the searched for minimum, too, so I considered this appraoch suboptimal and came up with a different derivation routine.
If the data sets aren't too large (yours are very small which doesn't make things easier as we hardly can smooth) and you don't run into problem with oscillations introduced by the spline interpolation, the interpolation approach may be the more stable one. You have to try out with a bunch of sample data how it works out.