What would happen if one of the syndicate shot, say, a bean goose by mistake and was prosecuted? Would I be held responsible?
No. Individuals are personally responsible for what they bag when game shooting and if something was illegally shot by mistake the shoot captain could not be prosecuted.
However the shooting of protected species or of quarry species out of season is a highly emotive issue and if it happens brings the sport into disrepute.
Well-run wildfowling clubs have an induction period for new members specifically to avoid the risk of this sort of error being made.
As your syndicate operates in a sensitive area it would be sensible for you to do something similar.
There is one golden rule that applies in all circumstances – don’t shoot unless you are certain your target is a legal quarry or pest species and is in season.
A more serious risk from your point of view is that the landlord might withdraw permission to shoot if an identification error was made.