Indesign aligns inline objects to the bottom. Is there a way to make it so inserting an object inline will make everything go to the top instead? I can manually accomplish this with baseline shift, but I'm looking for something I can attribute to a paragraph style that will responsively change based on the size of inline objects.
I can't tell show you a fully automated way to do this, but I have something better than using baseline shift: simply move the inline objects.
What happens when you paste an object into a text frame isn't really that it "makes things go to the bottom". Anchored objects by default simply sits on the same line as the letters. The anchored object must stay inside the text frame, so the whole text line moves down to make room for the anchored objects.
A way to make the anchored objects hang below the baseline is to first drag them down too much to make the text move all the way to the top and then select each one of them and set their top Y-coordinate to match the top Y-coordinate of the text frame. (Sadly the anchored objects won't snap to the top of the text frame.)
If you enter more text in the text frame it will go through the anchored objects. This can be fixed by applying Jump object text wrapping to the anchored objects.