Should grass cover be planted on rows and between the vines?
Grassing between the vine stocks is possible. Competition is fairly limited as the surface area planted with a grass cover crop is small compared to what it is inter-row. Also, given this particular location, the vines' roots probe deep into the soil. If a grass cover crop between the vine stocks is desired, pilosella hawkweed (Hieracium pilosella) is a good option. Whilst it appears competitive, it skims the soil and provides good coverage and shelter.
Other species such as subterranean clover, downy brome and barley have allelopathic properties that further limit weed growth. Some leguminous plants such as strawberry clover are also good candidates for planting in between the vine stocks, though they are not very long-lasting. Other trials are being carried out on sedum and thyme species. It would appear that pilosella is the best suited crop for this purpose, despite the transplanting process to plant it being particularly time-consuming.