Is it possible to keep the key of a piece of music in the Octatrack, if I increase the original tempo?
Yes absolutely. There are a different options for timestretching.
Once you cut/slice your wavs up and make sure all the tempo information is correct in the sample settings page - you can select either “normal” time stretching or “beat” depending on the audio material.
When you change the tempo the real time stretching algorithm kicks in. It’s a bit hit and miss with quality - some sounds work better with it than others. I find long bass tones don’t work well, but leads/pads and other stuff works near perfectly.
If your bass notes are not sounding good timestretched you could turn timestretching off and use loop points instead.
You can also select “none” as well, which is handy for drums. So when the tempo changes the drums don’t stretch out.