The old school method of pitch adjustment is to change the speed of tape playback. In other words, record it on tape and then speed up the tape motor until it's in tune. You can figure out just exactly how to re-tune by recording a single note and then playing it back and slowly speeding it up until the tuner says the note is in tune.
There are tools in the digital world to do something similar. In a sense you are then doing two steps at once...
1. Speeding up playback
2. Time stretching to keep playback duration the same.
As you may know when you set up a track for good time stretching, marking transients can really help the algs that do the time stretching.
Interestingly, there is a RME tool for pitch adjusting through the UCX interface I have. I can detune up or down maybe a 1/4 step.
I haven't really helped you, but it's the best I've got.