Low carbers could cut down on the sugar or omit it altogether and sub swede mash or fennel and celeriac mash for the potato mash.
Recommended pheasant purveyors:
Wild & Game
https://www.wildandgame.co.uk/
Nationwide retail and wholesale delivery
Stour Valley Game
http://www.stourvalleygame.co.uk/
Local delivery in East Kent, shop. Farmers markets in normal times.