Some thoughts on both threads - OT and Refs - 4 refs who actually call the
rules and a 4 v 4 in OT.

How would this change the play?
Taking a penalty is more costly since you lose 1/4 of the non-goalie skaters
instead of 1/5,
Seems it would encourage the ref to bury the whistle since a call would be
more costly.
More rest for players since only 4 on ice for each shift.

How would this change the referee recruitment, training and selection
process?
A bigger pool would be needed and thus there might be more talent at the top
once it has had an opportunity to work for a while

And a new topic-  Selection and assignment of referees to the tournament
games??
Can it be improved even if it stays at 3?  For example, go for the best
officials without regard to conference affiliation.