If you have the warranty I would highly suggest using it, even though they are going to try and give you the run around. Document everything keep pressure on them.
Having said that, the 5.3L w/4T65E trans have been known to have a very high failure rate. I would say that your torque converter has taken a crap on you. It's the same converter that is in the HD trans in the supercharged cars but was never really intended for the V8 with DOD. While cruising and the car goes from 8cyl to 4cyl mode the TCC has to unlock and lock for this function to happen. This has been known to cause early failure and has similar symptoms to what you are describing. On top of all of that the 5.3L version has been known to have horrible cooling for the trans and never helps the situation. Edit: should also add that when the torque converter fails it throws material through the trans which can clog the filter like you're seeing. Classic symptoms where you have no gears, shut off the car and restart and then all of a sudden you have gears back.
Better converter along with valve body upgrades is going to be your best option at the moment, but that always costs $$$$. Dealership with replace everything with the same inherent weak points and send you on your way. Upgrading is the way to go if you plan on keeping the car.
