Toilet Tank Movement
If you cannot tighten them much more by hand then don't do it - I've cracked a toilet tank by overtightening because one side seemed to insist it be higher than the other side. . . believe me, once there's tension it doesn't take much more - just one more twist - and then CRACK!
So - I think you should consider giving the back resistance from behind - How possible would it be to remove the tank and install a series of shims or a thin layer of wood to the wall behind it to "move" the wall forward and make contact - thus - taking away the wiggle room?
At this present moment in time I am making cabinets for the kitchen - just in case you wanted to know what I'm doing when I'm not around.