If you still have the installation booklet, you can read Step 3 Toilet Bowl Installation (This is as appears in my Toto Drake booklet) It is possible the Drake II is arranged differently. It explains that there are 3 points of contact that will actually contact the bottom of the toilet tank when properly installed. One point is front right, one is front left, and the third is back center. The two mounting bolts should be tightened alternating from bolt to bolt to keep the tension even until the three points make contact. When this is done, the tank should be rock solid. No modern floor mounted toilet requires wall contact. In fact, if your toilet did mount that closely, removing the tank lid would be difficult. My Drake has over 2 inches clearance and it is mounted on a 12" rough-in...exactly 12". So, don't worry about the 3" you have, it's fine. I think you should check the 3 contact points and tighten the bolts more. Some advise using a piece of paper between the points on the tank and bowl and quit tightening when the paper starts to bind in the gap. Under no circumstance should you shim or improvise anything to go between the tank and bowl. It might be helpful to read the "Sticky" at the top of this forum on Drake installation.