Nate, I could be wrong, but I think you might want to support the engine from above so it doesn't hang down when you remove the transaxle, because the transaxle helps hold the combination engine/transaxle in the car.

I cut and pasted this from some random site, I don;t know if this affects the year Saturn you have, but it might be the cause of your problem:

CONDITION:
Some automatic transaxles may have harsh and/or erratic shifts, no gear or gear stuck on, and the malfunction indicator lamp (MIL) (SERVICE ENGINE SOON telltale lamp) may come on, and multiple diagnostic trouble codes (21, 22, 23, 24, 25, 75, and 78) may be stored in the PCM/TC.

CAUSE:
Some automatic transaxles may have been manufactured with iron sediment that migrates to the control valve body assembly causing transaxle control actuator valves to seize and or the valves in the control valve assembly to stick or be sluggish to move.

GM recommends everything from flushing the transmission to transmission replacement to correct this problem. There is really nothing you can do to test for this condition.