that emits 1.5A of 5V in a best case scenario. A Pi 3 wants a good 2A+ of power; the official 2.5A power adapters are a good bet. I would not go near trying to run this off your Eurorack’s power supply.
Beyond that, it’s a meaty project. The Pi’s own USB and similar connectors are located on the left edge of the Norns shield. You’re not removing them, so you’ll need space on the left to run extensions. Have a look at the various photographs of the shield mounted on a Pi in the main thread. Where will your “extensions” go?
Audio jacks are more doable: they are on the top edge. You could, and I would absolutely not advise this, desolder them and wire up your own harnesses. Then you just have the problem of amplifying and attenuating output and input respectively. The latter is straightforward; the former is not always easy dependent on volume.
Norns is designed as an external, desktop unit, and it works really nicely as that. You’ve perhaps made the mistake of seeing something electronic that is shorter than 3U, and deciding it needs mounting in your rack. This is not always the case.