2007 Hyundai Accent Reverse Gear Problems

Anyone with thoughts on what might be causing my problems with shifting into reverse? Since new, about 1 to 3 times/week, when shifting into reverse, one of the following happens: 1. Gearshift lever gets stuck; 2. When I let out the clutch, there's a slight grinding noise and the car doesn't back up, but when I depress the clutch, the gearshift lever moves about 1/4" without my touching it, then, when I let out the clutch again, the car backs up normally; and 3. When I let out the clutch and start backing up, the transmission pops out of reverse. Dealer service writer reported difficulty engaging reverse, but others at dealership, as well as Hyundai area technicians, all deny encountering any problem. Hyundai denied warranty claim. I've been driving manual transmission cars for 55 years, and my last car was a 6-speed, so I don't think I'm causing this.