I have had some success in removing the adhesive residue off the face of overlapped stamps. Many years ago I worked in auto body repair and painting. We used a product called "Wax and Grease Remover" to prep a car for painting. I used Ditzler brand auto refinishing products. It does not dry as quickly as thinner (and is not a thinner) but does dry eventually. That it evaporates slowly may be why it worked so well for me in removing adhesive from stamps. (It is also great for removing chewing gum from cloth.) Unfortunately, it did not come in small cans. I bought it in gallon size, but it might be available in quarts. For where to buy, look under "Auto body paint and supplies" or similar wording in the yellow pages. Mineral Spirits might be a substitute but I never tried it.
CAUTION: It is a flammable liquid and you must have adequate ventilation. Kids; do not try this without adult supervision.
Disclaimer: The following procedure may cause damage to the stamp paper or may smear the ink of some stamps. It may remove tagging or other coating on the stamp.
Test an identical junk stamp first!

First soak the stamps to separate them using my soaking tips post or you own method. After soaked and separated, rub the surface of the stamp gently, using a slightly moistened white cotton cloth. If the overlapped adhesive is only on the edge of the stamp, a Q-tip moistened with the remover can give great results without rubbing on the design.
A much safer procedure but less successful is to lightly pinch a damp stamp between two fingers and "pull" the adhesive off with a motion towards the edge of the stamp. It has been most successful for me when the stamp only is damp but not wet or completely dry. The adhesive rolls right off the stamp sometimes stretching like a rubber band. But use caution or you may pull the stamp itself apart. Again, practice on junk stamps.
Marty