Sound deadener in the cab corners...?

[mfm3]

Removed the in-cab tank and now swapping out the carpet. Looking for advice on what to do with the inside corners. Should I use sound deadener mat in this area or are there better options? Also wondering if there is any reason not to add sound deadener to the back wall of the cab. I have a piece carpet that will cover the back wall.

Would also like to see ways to make the space behind the seats usable for storage, although I don't know what I would need to put behind the seats. Maybe a set of jumper cables, fire extinguisher, small toolbox, etc.