Nothing wrong with the trimatic, just ask any drag racer whose on a budget and want a strong and light auto behind a high horsepower motor.
Anyways, the trimatic operates on a vacuum for its kickdown. So it could be a problem with the vacuum line, blocked or a crack in the line somewhere.
But by the sound of it, it'll be more something internal between 2nd and 3rd, i'd say the clutch pack is slipping.
Whats the trans fluid like ? It needs to have a red tinge to it, otherwise dump the fluid and re-new it.
Apart from that your best bet would be to take it into a transmission workshop and get them to have a look at it.
If your planning on moding the 4k, you can also get the auto rebuilt to suit the motor.
Stronger and thicker band between 1st and 2nd, different clutch pack between 2nd and 3rd, change the servo for when the gear changes happen, the gear changes can also be changed for how hard/soft and fast/slow the gears get changed. The torque convertor can also be swapped for one that suits the motor's rpm range. Even the gear selection can get modified - keep it self shifting or do the shifting yourself.
If your interested in bit of drag racing, the box can setup for a trans brake.
I wouldn't class the box as boat anchor.