There's two things to consider here:
#1) It seems like Johnny's dad is not concerned with Burke himself, but with Burke's interest in big players and a perceived low confidence in smaller players like Gaudreau. I don't think Johnny's dad has a problem with Burke personally. This is a good thing; it suggests a level of understanding that needs to be bridged, and likely can be.
#2) If there's any one person to go put a bunch of confidence in a player and his family, it's Burke himself. He's probably on a flight to New Jersey as we speak in order to talk to the family. This isn't something Burke seems like he would put off.
Burke always speaks glowingly about Gaudreau, expect for his size (which he doesn't say flat out bad things about anyways). Burke has also gone on record saying that he is fine with small players in his system, as long as there's bigger players to surround them with. He's said this.
He probably signs, in my opinion. Burke will get it done.
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