Does DNA Ligase look for complementarity in sticky ends?
If I understand correctly you are preparing your cloning vector by digesting it with two enzymes that are 31 bp apart. If you have a high background of recircularized vector see if there is a unique restriction enzyme site within that 31 bp.  If there is, and if the fragment you are trying to insert also lacks that site, then a simple approach would be to inactivate the ligase, and digest the reaction with the third enzyme.  That should drastically reduce the background of recircularized vector.
If after gel purifying the vector backbone after the double-digestion, you get a  significant background of recircularization, then you can easily test your hypothesis about ligase ligating mismatched sticky ends: both of the starting sites should be gone and any sites in-between them should be gone.  Have you tested this?