Just making sure you're checking it correctly. Startup, shift back and forth through the selections, and immediately check the fluid level while running, using the cold marks. If you checked it correctly, and the fluid was overfilled by a quart, that will typically cause air bubbles, and is definitely not a good thing.
Just confirming that in P or N the engine will consistently idle, rev high, and then come back to idle normally. If that's correct, and it's only able to do 1-3 MPH, then that's not limp mode (which would be up to 20-30 mph). 'Growling and grinding' is definitely not good and sounds much more like gears. You can confirm that by removing the tranny fluid pan, where you're likely to find metal fragments. If so, that's definitely a new transmission. No idea about the engine, but a compression/leak down test is probably a good thing to do at this point.