Advice on tidying up opened fireplace

[Flyfisher]

Also, Cubist, that Chimney Sheep looks good and easy in theory, but will blocking all draughts not lead to more problems later?

An alternative might be a chimney balloon: https://www.chimneyballoon.co.uk/ These are designed to allow a certain amount of airflow.

We used one in a previous house for a chimney that suffered quite badly from 'reversal' (mainly in the non-winter months, strangely) and it definitely stopped cold draughts coming down the chimney so I assume it would also minimise heat losssed up the chimney as well. Ours was a slightly different design to the one in that link but the principle was the same - blocking most of the chimney but allowing a trickle of air around the corners where the basically spherical design of the balloon could not make a perfect seal.