I would be tempted to get some covered, lockable skips for some of your regulars. Weld a BIG padlock to it on a chain, then give them a key and paint their name on the skip. If they want to drop off their shred after hours they can do and you get to stay in bed. They could then come in the next day, bring their ali, copper, etc and cash out. It would work on trust, but it might save your sanity. On busy nights they can then do multiple runs and bring in greater volume. The other option would be a 40 foot container with doors each end. Weld a partition in the middle and you have two spaces for drop offs. You would have to put skip or something inside it though so they could dump their shred in it otherwise you would have to drag it all out by hand.
Next time some skips come in for scrap, it might be a better use of them, or certainly worth a trial run.
Just do it in a way that someone can't lift the entire skip and steal everything.