Thanks for sharing the PicoScope 5 file. I agree that you need negative value in your current probe ranges. Neither PicoScope 5 or 6 come like this out of the box. You have to modify the ranges yourself or get a file where someone else has already done it. Best to learn how to do it yourself. The procedure is quite different between the PicoScope 5 and 6 versions. Personally, I think 6 is easier and faster to modify and create custom probe settings.
In your psd file, notice how your amp probe wave is fat at the bottom (until you zoom 20x). This is because your custom range has no negative current value. The amp probe was not zeroed exactly and went a bit negative when there was no current flowing. This is easily remedied in PicoScope 5 by editing the range under Settings/Custom Ranges. Just put some negative value there for that 0-20A range. Make it say -5-20A...or whatever. or create a new range to suit.
PicoScope 6 doesn't show any waveform outside of the scaled range. This isn't a software problem. It's a user issue. You still have to make a range appropriate for the signal.
Thanks for your vote of confidence. As you know, we cover all these issues and procedures for both PicoScope 5 and 6 in our training. We provide comprehensive PicoScope automotive training to users world wide. Our PicoScope training movies are available to our group via web delivery and on CD.
Here is an example introduction to PicoScope 5: