I ran archlinux using the software and kernel in that repo for my surface pro 4. It worked great. Additionally I found GNOME desktop to work well, particularly with some extensions like toggles for rotation, on-screen-keyboard and other stuff you'd find on a phone. I also setup pop shell and cosmic for tiling window management, but paperWM might be better for this these days.

I should not that I had some troubles with the stylus. Sometimes it would work, sometimes not and if I used configuration tools it would sometimes help or sometimes make it worse. That said, I think my stylus is a little screwed up. There is a lot of good info in getting the stylus working and troubleshooting it, you should be able to get it working, for me it was always just a matter of time before I had to fuss with it.