727 slipping

How come it took until post #16, for the KD adjustment to be questioned. That should have been post #2.
KD is a misnomer. It should really be called Throttle-Pressure Adjuster.Cuz that's what it does. Sure it provides a kickdown, but that is secondary to it's function.It's primary function is to increase line pressure, which directly increases the holding power of the clutch packs and servos. Secondly, it delays all the upshift speeds, by suppressing the shift commands coming from the governor.
If there is insufficient line-pressure, the clutches slip, and the tranny shifts softly,and very early. With line-pressure maxed out, the shifts will be harsher and much higher up the speed range. The end result is that you, with the gas pedal, can control the shift timing and harshness, right from the driver's seat, in accordance with the current driving requirements. Yeah it kicks the tranny down a gear, but that is just the pressure balancing act going on inside the VB at all times.

Long story short is, get after the TPA, ASAP. It may already be too late, but it's worth a shot.