Re: 01 Grand Cherokee Limited 4.7
Welcome to the garage. I would first check if the rigging of the shift lever is correct. Just remove the shift cable from the transmission and check with the shift lever in P, if it lines up with the transmission shift lever in P (rearmost position on trans lever).
How is the transmission fluid looking? No burnt smell or black fluid?
Eventhough this transmission is electronically controlled, reverse is completely mechanically. The shift lever just moves a mechanical valve inside the valve body. Two clutches are pressurized to engage reverse, The Lo/reverse clutch, which is also used for 1st gear, and the reverse clutch.
If you would have to change the transmission, there is indeed no difference in between the 45 or 5-45 RFE transmissions. The only difference is the programming of the TCM.