Okay, there was a simple answer to this in the end, although it took me a long time to find it. I started by trying to intercept touch events and failing, which eventually led me to realise that I had added the site to Compatibility View (Settings -> Compatibility View Settings), where I also had checked "Display intranet sites in Compatibility View" and "Use Microsoft Compatibility lists").
I think this reverts to the site displaying in ie7 mode. Due to this, I think there are issues with the MS-touch commands being recognised, and so -ms-touch-action: none was having no effect.
To be clear, then, referencing touchpunch, whilst also using -ms-touch-action: none, should get the jQuery sortable functionality working in ie11 - just be sure to check your compatibility settings!