Recently for me this has really become a problem and I would hardly say that both my material and data storage are excessive. I agree that something has to be done, whether it is by means of station lockers or module expansion. Hopefully we see a solution soon.
Dump all the low grade easy to find mats. There is pretty much 0 reason to hold on to Iron, Nickel, Sulphur, Phosphorus (keep 3 of these if you're on a planet) Carbon, Weak Shield Emitters, Shield Emitters, Flawed Focus Crystal, Focus Crystals, Conductive Components, Distorted Shield Cycle Recordings, Inconsistent Shield Soak Analysis, Anomalous Bulk Scan Data, Any of the wakes except Datamined. These can all the gotten just by looking sideways at any ship.