Reza Hadavi suggests BamH I/Hind III because they should release the band even if the EcoR I site is lost upon subcloning (per your own reasoning).
I know it's a long shot, but is there a chance that your minipreps are dirty? In the old days of DIY reagents it was not uncommon to get plasmid DNA amplifiable by PCR, but refractory to restriction enzyme digestion.
Also, is there a chance that you are getting false positives in your colony PCR? What controls did you set up?
Double digestion should help resolve your problem, Try including a known plasmid DNA that would release a fragment to make sure your restriction enzyme set up is working as expected. If these don't resolve your issue, I suspect your competent cells are contaminated and carry some other plasmids. This non specific plasmid could be another reason why you are getting PCR signal in self ligation colonies.
Let's focus on your insert first. How many restriction enzymes did you use to prepare your insert? If one you should dephosphorylate you digest plasmid to prevent self ligation. Happy New Year to all here B-)