Ditch the Chiltons and get a Toyota manual.
Did they leave the engine in the car when they pulled the trans?
Or did they drop it too?
It's pretty easy to get the trans on with the engine out.
Leave the Tcase on.
Rotate the trans counterclockwise so the Tcase can pass the ear of the block.
Once it's past the ear, rotate back down and line up pins/bolts.
The trans has to be flat with the engine too, if it's crooked the input shaft won't want to slide into the clutch disc.
Also, it helps to have some strength, it's easier if you can manhandle it.