The LX470 suspension is rough but nothing like "beating to death".
This is having 3 different brands of tires what is most likely causing a bumpy ride. This is also a huge safety issue. In my region, we've recently had a driver who died as he was driving at circa 60mph, had to make a sudden maneuver but was unable to retain control of a car due to different tire threads and their different level of wear and tear. He smashed into a truck and died.
Not ideally, but you can still have front/rear tires of a different thread pattern/wear and tear, however, both of the front tires should have the same pattern/wear and tear and both of the rear tires should have the same pattern/wear and tear (and you'd put the most worn tires on the rear axle). Ideally, all four tires should be the same.
Other things which may cause a bumpy ride are:
- dirt on the wheel disks. Not your case (having driven 300 miles, the dirt must have gone away);
- a wrong wheel alignment. Best to perform a wheel alignment once a year.