My 1992 2.2L AT Camry shakes really hard accelerating through 45-60mph.
I can feel it wobble a little at lower speeds, it's more subtle and
seems to follow the wheel speed.

I had all new tires put on, didn't help at all.  I suspected the engine
mounts since the dogbone was shot, so I replaced the front (totally
shot), rear (seemed ok), and dogbone.  This helped just a little, the
shaking is still really bad.  There isn't any clicking when I turn, so
I had ruled out the CV joints, but I took a peek anyways and replaced
the intermediate shaft bearing (blown) but that didn't help.

I did notice that on the driver side that the tripod case, the part at
the engine end of the shaft just before the tranny, was really sloppy
in the transmission.  Putting my hand on the tripod case i can move it
1-2cm in any direction.  Is this likely the cause of my problem?  It
seems strange that parts in the transmission would be able to move so
freely.

Thanks for any ideas or suggestions, I've run out of possibilities at
this point.