We present a novel method of constructing streamlines to derive wind speeds within jovian vortices and demonstrate its application to Oval BA for 2001 pre-reddened Cassini flyby data, 2007 post-reddened New Horizons flyby data, and 1998 Galileo data of precursor Oval DE. Our method, while automated, attempts to combine the advantages of both automated and manual cloud tracking methods. The southern maximum wind speed of Oval BA does not show significant changes between these data sets to within our measurement uncertainty. The northern maximum does appear to have increased in strength during this time interval, which likely correlates with the oval's return to a symmetric shape. We demonstrate how the use of closed streamlines can provide measurements of vorticity averaged over the encircled area with no a priori assumptions concerning oval shape. We find increased averaged interior vorticity between pre- and post-reddened Oval BA, with the precursor Oval DE occupying a middle value of vorticity between these two.