Turns out sometimes it’s actually better to try than to read hundreds of tutorials. I was already about to adjust UIDs on the Vero because of dillthedog’s post on NFS with Synoly, but decided to try before messing up everything.
Long story short: Even with DSM 6.1, it’s enough to set up NFS permissions according to the Kodi wiki, create mount points in /mnt on the Vero, and mount these in fstab with noauto,x-systemd.automount 0 0.
Everything’s working fine now. Even files with bitrate peaks of > 100 Mbit/s play smoothly.
Thank you for the support and for building great soft- and hardware! 
