It's not a k04 problem.. It's an APR in general problem. Overall I like their tune, but I've had this exact issue since 2008 when I was on v1 of the very first tsi tune, and I've had it off and on since. Been through about 8 different versions of tunes as they were up graded, multiple intakes, aftermarket clutch, intercooler, new intake manifold, carbon cleaning, multiple methanol systems, multiple downpipes and exhausts, stage1, , stage2, k04, multiple versions of each etc.
If you catch it on a log, the throttle position stays 100%, and the throttle plate after a quick on/off throttle to shift, the throttle plate goes to about 20% for about 5 seconds if you keep your foot in it, and it ramps slowly to 100% like nothing happend. If you pedal it, its gone immediately, but still fucks up your run. It's super annoying. I think the only way around it would be to go with the NLS option, but I'm not sure if anyone has tested that