I have exactly that problem, i used to always use the same grip left hand over right hand under, i also found myslef twisting too much and letting the weights hit the floor unevenly. Ever since i changed too a more regular grip both hands over i have found thqat my technique has improved a lot with the weights hitting the floor at thea same time.
just keep switching the grip around on alternate sets, i use the overhand grip untill the weight gets heavy then switch to alternate, another thing i do on occasion, is to start the bar on pegs about 2 feet off the ground and do the lift up/down and return it to the pegs,...it is not as hard as it sounds