They leave our centre-back free and we still refuse to carry the ball

I’d make carrying forward an expected solution whenever the opponent refuses to engage. If their block protects midfield and leaves your centre-back free, the centre-back should be able to travel until somebody has to make a decision. The moment an opponent steps out, the pass they were previously blocking may become available. I’d train it in a build-up game where the centre-backs score a point for crossing a line under control before passing. That gives them permission to recognise the space rather than treating every possession as pass-first. The detail is not “dribble as far as you can”. Keep the ball on the safe side, scan while travelling and be ready to release as pressure arrives. A centre-back carrying ten yards can change the whole opposition shape. If nobody presses, keep travelling. If somebody jumps, find the player their movement has freed.