Yeah, its not actually a kickdown, and it has everything to do with upshifting. It adjusts the pressure at which the transmission operates, and moving it even one tick in either direction off of the perfect position can make it shift too hard, or too soft.
Basic rule of thumb I've noticed is to set the cable as close to the firewall as it'll get, then grab the throttle linkage by hand, and open it as wide as it goes, the cable should pull out a bunch. I've typically found that one tick back towards the firewall is about perfect with both my 700r4 equipped vehicles. To test it, you should be able to punch it at about 40 mph, and still have it downshift, and it should drop into OD at about 45 mph with light throttle.
Make sure you get whatever it is fixed ASAP though, cause long slow shifts like that will kill your tranny in a real hurry.
If the TV cable has no effect, then you'll need to have the valvebody looked at. Sometimes the valve bodies wear out with age, and make the tranny shift sloppy, even after an overhaul. Most tranny shops don't touch the valve body during a rebuild, less it's gasket. It cost my buddy 150 bucks installed to have the valvebody overhauled after his freshly installed tranny continued to slip.