Dextron VI was first used in 2006....not sure if all vehicles got this at the same time......
Your dipstick saying III, means one of two things....either your vehicle came with Dextron III because the vehicle was not one of the first to have the new fluid, or the vehicle was assembled with a new tranny, but it could be a surplus tranny from 2005......the other possibility is, the wrong dipstick, but I doubt that.....
In either case, Dextron VI is what you should be using.....
As for the slip, the only way to know for sure is have the PCM scanned for tranny codes(not all codes immediately turn the CE light on), or have a road test done with a scanner reading slip rpms(should not exceed 25-50).....for example, some codes will have to fail on two consecutive drive cycles....so if it fails on one, and the next drive cycles either it doesn't fail or doesn't run, the counter starts all over again, where you have to fail twice in a row to turn the light on.....while the light might not be on, a code will be set in history....so if you think you have a problem, have it scanned for codes....Places like Autozone do it for free.....