I have thought of this, and that obstacle can be overcome through four points:
1: the umbilical-cord like tendril could grow (albeit slowly), extending the length; the tendril could also just be really long (even ~50 ft)
2: the plant supplements the animal with photosynthesized nutrients (as you stated)
3: a slow metabolism and/or something akin to hibernation when food is scarce
4: rationing; i.e., the sheep only eats a small amount at a time, or only in a specific area within its reach, allowing forage to regrow
These combined should be enough to prevent starvation