Hi.
I do run TVheadend with HDhomerun EU (4 tuners - “dvb-c”), two dvb-t sticks on an ubuntu linux. For a while I mounted the Synology NAS share via NFS to my ubuntu filesystem and made this the record folder for tvheadend. Works.
I decided to use a local HDD instead, as potential recordings always interrupts my maintenance work on the NAS… I can ask family members to pause a watching, but I can’t ask the cable provider to wait with the movie… 
Also I use the “manual” job of coping a tvheadend record (which I do in MKV), to adjust the filename for better finding with the universal movie scraper in Kodi. On Kodi systems I do have the NAS shares mounted and use the “advanced settings” to link to a mysql database on the NAS. As a result only my central Kodi does rescanning of network folders to find new movies, but all Kodi’s will get the information from the central DB.
If any element of my setup is challenging you, please feel free to ask and I can be more technical detailed…
Thanks,
Oliver