TIA for viewing my thread.
This car runs super smooth besides these 2 problems.
1. Car will not shift if accelerated more than lightly. It will continue to increase RPM up to ~4.5k RPM and then just drop. It gives up and I have to let off the accelerated for it clunk into the next gear.
2. From 50mph@ ~1.9k rpm to 65mph@~2.5rpm it will do a moderate to light intermittent stutter (every 2-4 seconds) while in cruise control or just constant speed. I do not see any change in the RPM gauge when this happens.

Those are the only problems I have with the car. When lightly accelerating, it shifts just fine under 3k. Moderate acceleration is when the transmission doesn't want to shift and starts to clunk into the next gear, only after I let off accelerator. I have no problems with car when lightly accelerating through the 50 to 65mph range. The stuttering only takes place when holding a constant speed in that range.

Things I have done since ownership (1 month owning and had this problem when purchased).
1. Timing belt/ Water pump + oil seals
2. Oil change/ filter
3. Coolant system clean/ change
4. Valve cover gasket change
5. ECT (car started to stall at stop signs or parking/ now fixed)
6. ONE ATF drain and fill (~3 quarts, i believe)
The ATF was practically black water. So far, I have only done one drain and fill since I decided to ask for advise before doing more.

What should I do next?
Finish ATF drain and fills until it is a nice red color?
Start changing transmission solenoids?
Something else?
OR is it a lost cause and just wait for the transmission to poop out and get a rebuilt one?
TIA for your help and advise.

 

If the trans is the causing the shutter it may be related to the torque converter.

However suggest trying to determine if the issue is something else.

Rotate the spare tire in and determine if this changes the shutter.

When driving, move the steering wheel slightly one way or the other to shift the cars weight between sides. Determine if the shutter or "road noise" changes perhaps the result of a bad bearing.

At low speeds make sharp 360 left and right turns listening for clicking, popping noises from the front axles.

Can you feel the shutter through the steering wheel or when you apply the brakes?

As to shifting issues. Disconnect the electrical plug going to the trans. Then drive manually shift through the gears using the gear shift.

Determine if the trans up shifts under throttle when moving the gear selector from one gear to another.

Could be the throttle position sensor, a shift solenoid inside the trans which controls fluid pressure (No 1 or 2), debris in the fluid body passages.

How is the speedometer needle indication, steady and normal or wobble?

The only adjustment with the trans is the kick down cable which manually transmits throttle position to the trans by cable position. Check adjustment.

When changing trans fluid. The best way is to undo the trans fluid output hose from the radiator cooler and run this into a container. With engine running the trans pump will force out the old fluid. Stop after about 2 quarts then refill trans. Repeat the process until the fluid is clear then if need to off. This replaces all the fluid with new.

It is possible but rare the trans intake screen is plugged but extremely uncommon and if plugged with debris there is major issue with the trans.

The internet has LOTS of detailed service information on this trans A140E.

 

Thank you very much, toyomoho!
After I bought the car, I put on new tires all around. Unfortunately, my current spare does not hold air. I did not check the spare when I bought the car. The issue was present then.
But I will rotate the ones I have on now and see if it does anything different.

When I bought the car, I did the 360 turns and did not have any popping, but I will try again later this afternoon.

The steering wheel does not seem to be affected by the shuttering. The car does a quick shake. I thought it was the transmission because it kind of feels like the transmission is trying to choose between 3rd and 4th. It does not have the same effect through the 50-65mph range. It shudders the most when close to the 50mph.

Ex. I'm driving with cruise control set to 50mph. Then I reach an uphill bridge, not very steep but uphill. When it starts going up the hill, it is fine. When it gets to a part where it feels like it should shift gears, is when it gives me the most stutter effect.

It still does it through the rest of the 50-65mph range but not as bad. The most effects are when I reach uphills or downhills.

As for the speedometer, it is very steady.

I will do the the electrical switch disconnect in the afternoon.

And thank you very much for the tip on how to change the trans fluid. I will do that as soon as possible.

 

If you think the trans is shifting between gears, is the RPM changing?

The trans should have a O/D switch that turns on/off the torque converter lockup function. Try operating the car with the switch off (light on at dash).

Check transmission kick down cable adjustment. Runs from throttle pulley at throttle body to trans.