The 45RFE does not use bands to operate. Its all clutch packs to hold whatever gear its in. I personally have not looked much into them but the RFE (rear wheel drive, full electronic control) is nothing like a 904/727 based transmissions of years past. Lots of special tools called out, basic kits are a couple hundred dollars and up.

You may look into a lower mileage used takeout or there are a few places selling remaned ones on ebay with warrenty support. Mopar remans carry a 3 year/100k warrenty, no idea about cost.

The RFE has been around since the 99 grand cherokee came out w/4.7 and it seems to be a decent unit, not heard of any widespread failures. The input & output speed sensors are on the driver side of the case (both same part also). You could try changing them and see if it helps anything. The transmission is totally dependent on an outside 'brain' to operate, garbage in=garbage out.