this is gonna suck to type ceause i have a seperated shoulder
but,
its either your boots worn down like this guy said, mainly your toe, check if its rounded off underneat the foot
or its the binding itself. what din does your binding go up to? 12 i think yo usaid? if you have it set at something like 10 or 11, thats too much. it will over time over stretch the spring and make it rigid and ineffective. sure it holds it in tight, but it has no give in any way and is very shaky and will develop play in it like you said.the solution is to get a new binding and, if you can, keep it at something low, like 6 or 7, when you're not skiing
or just get a higher din binding, like a 18 and keep it at 11 or 12 still. youll never pop out of it unless you're really big.
other than that, hte only other option is if the slider plate on the back of your binding is lifting off of the screwed in metal part
check if it lifts up at all
or if you grab the heel piece, if it gos side to side at all
if it does, you know thats the problem, but there isnt much you can do
remember though, redrilling a ski and fitting any binding, ESPECIALLY a new binding, (and plugging the old holes) is very compromising to the ski and can lead to a break very easily usally
good luck, and sorry for the spelling, once again, seperated shoulder.