I have to let off the gas pedal for it to shift to third gear

Welcome to 2CarPros.

The first thing that comes to mind is the throttle cable. Do me a favor, check it. Here are the directions for adjustment. The attached picture correlates with these directions.

Inspect and adjust the throttle cable.
1. Check that the accelerator pedal is fully released.
2. Check that the inner cable is not slack.
3. Measure the distance between the outer cable end and stopper on the cable.

Standard distance: 0 - 1 mm (0 - 0.04 in.)

If the distance is not standard, adjust the cable by the adjusting nuts.

Let me know what you find or if you have questions. Make sure the fluid is clean and full.

Joe

When the transmission was replaced, were cooling lines flushed? There could be something restricting line pressure. Also, have you checked for trouble codes that may be stored?

Let me know.

Joe

Welcome back:

Is it a different transmission? Was it serviced prior to use? For it to be doing the same thing, something has to be out of adjustment. Take a look through these directions related to the throttle cable replacement. Let me know if this is how you adjusted it.

ON-VEHICLE REPAIR
1. DISCONNECT THROTTLE CABLE
a. Disconnect the cable from the throttle linkage.
B. Disconnect the cable from the cable clamps in the engine compartment.
2. REMOVE PARK/NEUTRAL POSITION SWITCH. Refer to Transmission Position Switch/Sensor
3. REMOVE VALVE BODY. Refer to Valve Body; Service and Repair.

Picture 1

4. REMOVE THROTTLE CABLE
a. Remove the retaining bolt and plate.
B. Pull out the cable from the trans-axle case.

Picture 2

5. IF THROTTLE CABLE IS NEW, STAKE STOPPER OR PAINT MARK ON INNER CABLE

HINT: New cable does not have a staked cable stopper.

A. Bend the cable to ensure a radius of about 200 mm (7.87 inch).
B. Pull the inner cable lightly until a slight resistance is felt, and hold it there.
C. Stake the stopper, 0.8 - 1.5 mm (0.031 - 0.059 inch) from the end of the outer cable.
D. Install a new O-ring to the throttle cable.
E. Push in the throttle cable and install the retaining bolt.
6. INSTALL VALVE BODY
7. INSTALL PARK/NEUTRAL POSITION SWITCH
8. CONNECT THROTTLE CABLE
9. FILL FLUID AND CHECK FLUID LEVEL
10. ADJUST THROTTLE CABLE
a. Check that the accelerator pedal is fully released.
B. Check that the inner cable is not slack.
C. Measure the distance between the outer cable end and stopper on the cable.

-Standard distance: 0-1 mm(0-0.04 in.)
if the distance is not the standard, adjust the cable by the adjusting nuts.

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Let me know.

Joe

Welcome back:

I attached a picture below that shows what you can use. Dextron 2 or 3 are fine, and I believe Maxlife covers those. It should say on the bottle itself. I did note the following notice under a technical service bulletin.

NOTICE:
With the exception of mixing ATF Type T with Type T-IV fluids, different types of fluids must not be mixed.

I don't know if you mixed those. Since the trans is different, chances are you drained it but the converter could hold fluid if you used the same one.

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Now, I tried finding any info related to a late 2/3 shift. I cam across a technical service bulletin (TSB) that may be the cause of two transmissions doing the same thing. I had to attach it in two different pics. If you look at pictures 2 and 3, it explains an issue that is related to these vehicles. I overlapped the pics so you could continue reading them. Let me know your thoughts in this and if it seems to mirror what you are experiencing. I have a feeling it is relevant to this problem. Basically, the shift valve is pressurized with fluid from the governor on one side, and the throttle valve on the other. If something is sticking or worn, it will cause what you are experiencing. This valve is what routes fluid in the transmission to determine what gear the vehicle uses.

Let me know what you find.

Take care,
Joe