My toilet tank is right against the wall and the cover doesn't close correctly. I would like to tile the wall as well. Can I just buy a new wax ring and shift the toilet a half inch away from the wall?
Sometimes you can replace the tank bolts, washers, nuts, and big gasket, and tilt the tank a little bit forward, away from the wall.
And also replace the wax ring and try to scoot the bowl forward, as mentioned above.
Measure the exact distance now from the center of both the flange bolts to the wall, and provide that info.
Maybe the rough in is in limbo between 10 and 12 inches, due to sloppy install of the flange.
If so, going to a ten inch toilet would be easier, and you could still clean behind the tank, and the lid would not be too close or too far away.
And you could cheat it back towards the wall to eat up some of the gap.