Changing the solenoid pack for a repeatable single gear problem is always a good option if you don't have the equipment or a multimeter to test. A new solenoid pack will eliminate bad solenoids, clogged filter screens and bad pressure sensors, all of which need to be working 100% of the time to keep the TCM happy. Speed sensors are cheap too but will cause problems in multiple gears or your speedometer to act up.
Now if you have a multimeter I'd probably check wiring next because it's free and easy enough to do. I've seen issues were wires shorting together inside the harness would confuse the TCM. For example, my Sebring with it's original 41TE transmission started going into limp mode when trying to shift into 3th gear. The cause was the overdrive solenoid wire rubbed through the insulation and shorted out against the input speed sensor wire inside the harness. When the TCM energized the overdrive solenoid, the input speed sensor overloaded the stopped working and the TCM said nope I'm out, limp mode time. The harness looked completely undamaged from the outside so maybe the wire insulation was damaged during assembly or maybe the 400,000+ miles on the car finally caused the two wires to rub through.
To check the wiring, here's how I found my issue. Unplug the TCM connector and unplug both speed sensors and the solenoid pack connector from the transmission. Now get a multimeter and check for continuity between the transmission connectors' pins back to the TCM connector, each transmission pin should connect to a single TCM connector pin except the one main power pin on the solenoid pack connector, that goes to one of the pins on the EATX relay.
Now the important test is to check for continuity between each and every transmission connector pin with the TCM connector unplugged, there should be none. In my case there was a short between an input speed sensor pin and a solenoid pack pin and I instantly knew there was my problem without ripping any of the harnesses apart yet.
Alternatively, you can use a, borrow a, or pay a transmission shop to have them use their scan tool to check all the inputs and outputs for the TCM and monitor the data while driving especially when the transmission shifts into 3th gear. Here we are interested in the input and output speed sensors, current gear, commanded gear, 2/4 clutch switch state, UD clutch switch state and most importantly OD clutch switch state since 3rd gear is the first time the OD clutch gets engaged. When the 2nd to3rd shift is in progress data should show something along the lines of stable output speed, slightly lower input speed, 2/4 switch should change from on to off, underdrive should stay on and overdrive should change from off to on.
Good luck!