Another thing is that the time series appears to be hopelessly oversampled. Everything becomes much faster if you first resample:
Show[ListLinePlot[MovingAverage[ArrayResample[testData, 2500], 50]],
ListPlot[FindPeaks[MovingAverage[ArrayResample[testData, 2500], 50], 25], PlotStyle -> Red]]

One can put a bit more effort (calculate window sizes in the resampled data) into this, but basically one can then also determine where the peaks are for the original sampling:
peaksresample = N /@ FindPeaks[MovingAverage[ArrayResample[testData, 2500], 50], 25];
{Length[testData]/2500.*#[[1]], #[[2]]} & /@ peaksresample
Cheers,
Marco