The latest version of PicoScope Automotive will give upto a 1000 Sec/Div so if you set the software to this timebase it should get through the night on a long test such as the one you are trying to perform.
You can download the latest version from the following link:-https://www.picoauto.com/software.html
As for the current clamp, we dont see why this will not also get through the night on a long test. You will need to put a new battery into the clamp before you start the test but this should certainly be able to complete an overnight test.
I hope this helps to answer your questions.
Lee - Automotive Technical Specialist