We would probably look to our litter ordinance, which requires property owners to maintain their property free from litter, sock the owner of the vacant property with the fine of $100/day, and let them worry about suing the next door neighbor.
However, that does seem somewhat unfair, especially given the evidence against the big box (logos on bags, receipts, etc). You could try doing what our City Council considered recently: an ordinance that fines the person doing the littering as well as the person who provided the "litter," i.e. the person who produced the advertising.
The proposed ordinance language:
"No person or business shall advertise goods, wares, events, concerts, or merchandise by causing such advertising material to be thrown, deposited, or posted in violation of any of the provisions of this chapter. Any person or business that advertises goods, wares, events, concerts, or merchandise by causing such advertising material to be thrown, deposited, or posted in violation of any of the provisions of this chapter shall be guilty of violating this section along with the person so throwing, depositing, or posting the same.
There shall be a rebuttable presumption that any person or business advertised in any posting or the site of a concert or event shall be guilty of violating this section."
This applies directly to our litter ordinance. The target was leaflets advertising concerts. These leaflets are often posted illegally, or are the source of much litter Downtown. The goal was to hold the concert promoter and/or venue liable for the illegal posting or litter problem. The discussion led to liability for reciepts from fast food or retail stores, etc. and would they be liable as well, which resulted in the proposal being condemned to the indefinite pending list.