Probably a terrible idea, but melting the plastic and extruding the plastic in underground abandoned mines, filling up the empty spaces like icing on a cake from floor to ceiling. There are abandoned lead mines in Oklahoma, where the town was vacated because of the toxicity and the ground collapsing underneath. A place like that seems ideal.
In Finland one mine had broken the law and dumped all their waste in the back of the mine and they were ordered to clean it up and they raised their hands up and said they couldn't because it was too dangerous to work there. Govenment's mining superviser dude turned out to be paid by the mining company, surprise!
That assumes the plastic is already being collected, so why not just make new products from it instead of dumping it into the ground and then using even more oil to make new plastic?
Part of my reasoning is that it's also a form of carbon sequestering. Most plastic comes from petroleum, from the ground, and then they would be just putting it back in the ground. The deeper the better.