This exercise looks like it involves some subejctivity. For example, in the second plot, the "peak" on the left isn't really a peak at all, it's more of a plateau. Also, the only thing that distinguishes the peak near 190 from the ones near 290 is their relative sizes (which isn't even a precisely defined concept). So if you're going to do this, you need to figure out some measure of the "size" of a peak, and then pick a cut-off threshold, where you only look at peaks above the threshold. Needless to say, since it's a subjetive exercise, you need to figure out for yourself what the best way to do that is for your exercise.
That said, if I was doing this, I'd probably just play around with the different findpeaks options. You tried one of those options, but there are others (i.e., MinPeakHeight, MinPeakWidth, MaxPeakWidth, Threshold, MinPeakDistance) that you can use individually or in combination. Since there's no objective "right" answer here, you just need to play around until you're getting the behavior you're after.