I'm amazed you have Hebs with a condition score of 4.5! I've never heard of it, except perhaps on the lush grasslands of Cheshire. Hebs and other Primitives store their fat around their organs, internally, so the state of their insides is worrying. Finding that much fat on their spines and tail heads is weird to me. Are they pure Heb, or Zwartbles crosses?
I suppose the unusually warm autumn we've had, which has had the grass growing well into December may have contributed to their being well fed.
It sounds as if they are really digging into the bucket, so I agree that access should be limited to that.
Otherwise I've no idea - I've never had fat pure Hebs.
However, Hebs have the largest pelvic size ratio to their weight of just about any breed, so they can deliver large lambs including texel and suffolk crosses, easily.