The bigger pitch gives the goalkeeper more information, so I’d simplify the scanning process rather than the passing options.
Before the ball is live, can they identify three things: where the first line of pressure is, where the spare player is, and whether there is space beyond the press?
Then build practices where those answers keep changing. Sometimes the centre-back is free, sometimes the full-back, sometimes the 6, and occasionally the direct pass is the best option.
What I would avoid is a goal-kick routine where the goalkeeper knows before looking that pass one is always to the right centre-back.
You can also start possession games from the keeper under a time pressure once they are ready.
The objective is not quicker distribution for its own sake. It is earlier information.
If the goalkeeper scans while the ball is dead, the decision after the restart becomes much faster.
