Transmission advice

Hello everyone not new to the forum but new to the Grand Prix. Need some advice. I bought a 1997 GP GT with the 3800 and the 4t60e code m13. The guy told me it has transmission trouble, so I was aware of its problems ok. Here is the scoop. Trans shifts from 1st to 2nd fine, 2nd to 3rd you have to get up to about 50 - 65 mph before it will shift during this time I can feel something happen as if the trans shifts but nothing happens until you reach that speed. It is hard to describe the feeling its almost as if the solenoid has been activated but nothing happens. After it finally shifts to 3rd, 4th gear comes almost instantly. While driving home the first time I noticed no lock-up. Car has 167,000 miles. I did a complete filter and fluid change and pulled a cooler line and pumped through about 7 quarts to get rid of what was left in trans, fluid was a mess I don't think it has ever been changed. Also had a p1870 code come up on the way home. After fluid change the code has not come back and now I can feel the lock-up working as it should but still the same shift pattern. I added a bottle of Lucas trans treatment at fluid change. Anyone have a suggestion as to what might be going on, I am capable of going into side cover if I knew what to go after. By the way trans does not slip at all, and once you get into high gear it is fine. Any help would be great.

The 4T60E has a vacuum modulator to help control shifting and shift firmness based on engine vacuum. Just to be sure double check the vacuum line from the intake manifold and check the modulator out for proper operation, However, based on your mileage you may need a rebuild or a replacement transmision.

Forgot to mention that earlier. Line to modulator is ok, no fluid in line either. How else can you check the condition of the modulator valve? Thanks for the help.

What happens when you manually shift it from 1st to 2nd to 3rd and then into oD?

Same thing happens when you manually shift.