Strange Transmission Noise

[stl06corolla]

Hello all - I've got a strange problem that I'm hoping someone will be able to help me with. I've got a 2006 Toyota Corolla S with an automatic transmission. About a week or so ago, I noticed a vibration under my feet while driving 30+ mph. Doesn't matter if you're accelerating, decelerating, or coasting in neutral, the vibration is always there. I've had a bunch of problems with the tires on my car (Goodyears), but decided to bring the car to my local dealer to help diagnose the problem. They came back and said that I had a bad drivers' side front tire, so I went to the tire shop and had all four of them replaced (the back two I already knew needed it). When I got the car back, the problem was still there - exactly the same vibration that I was feeling before. I took the car home and set the front end on jackstands so the wheels were off the ground. I spun both tires and inspected for a bad bearing, tie rod end, ball joint, cv joint - all the usuals - with no luck. I then decided to fire the car up and run it in drive while the wheels were off the ground. Being outside of the car and close to the problem, I could not only feel the vibration, but I could hear a grinding noise. I tested both wheels in drive, and each wheel in drive one at a time, and noticed the problem in all scenarios. I then shut everything off and crawled under the car as it sounded like the noise was coming from where the axles enter the transmission. I checked both axles for play, and was surprised that I could move each at least a quarter of an inch up/down/left/right. I could also change the angle in which the axles entered the transmission. I had a friend start the car and run it in drive again with me underneath it, and I noticed that both axles had more than a quarter inch of wobble, and the sound was noticeably coming from where they entered in the tranny. As far as the tranny itself, the car drives absolutely perfect (other than this issue). I took the car back to the Toyota dealer, they had it all day today, and called me tonight and told me that there was no problem. I'm growing pretty frustrated because I know there's a problem, but my mechanical knowledge really stops at the tranny. I'm fairly certain it's not a problem in the drivetrain (bearings, axles, etc.), but I'm not sure what I can do from here.

Does anyone have any ideas on what I may be experiencing here? Any advice on what I should do moving forward (other things I can test)? Much appreciated!!