The slipping you are feeling could just be the torque converter unlocking.
The t/c will lock in 3rd or 4th gear. When you downshift from 4th to 3rd the t/c will unlock then if load and speed conditions are right it will lock back up.
If loads are high (throttle further open) it will stay unlocked to let the rpm's wind up to help acceleration.
how does it behave if you just leave it in overdrive?
Does it downshift from 4th to 3rd on its own on hills and does it still give you the same slip feeling?
The 4L80 is a relatively tough transmission, with a proper size fluid cooler and routine fluid changes it should last a long time.