Apron - two-step food connection
Barbecue - same, maybe 1.5 step
Bell - could use it to alert attention, seems two-step-y
Bowler - don't see it
Christmas - order things for presents
Cotton - don't see it
Court - order in the court
Doctor - could force you to do something
Game - games have rules, seems weak
Hole - don't think so
Judge - says "order in the court"
Jupiter - 5th planet in order, weak
Leather - don't see it
Mammoth - all species have a taxonomic order
Map - prevents chaos, mildly weak
Memory - recite an order from memory
Page - menus have pages
Pan - two-step food connection
Penguin - see mammoth
Pumpkin - see mammoth
Server - takes your order
Story - story has an order
Sub - don't see it
Taste - 1.5-step food connection
Van - could order a van
So I really like Court/Server/Judge. Maybe Christmas next. After that, gets really weak really fast.
Apron
Barbecue
Bell
Bowler
Christmas
Cotton
Doctor
Game
Hole
Judge
Jupiter
Leather
Mammoth
Map
Memory
Page
Pan
Penguin
Pumpkin
Server
Story
Sub
Taste
Van
Apron - Strong, IMO
Barbecue
Bell
Bowler - obvious yes
Christmas
Cotton - Strong, IMO
Doctor - They wear their little doctor beanies, but I wouldn't guess that here
Game - Lots of games have hats in them
Hole - baseball caps have the hole at the back
Judge
Jupiter
Leather - Is leather a common hat material?
Mammoth
Map
Memory
Page - I think this is also a kind of hat, but if I've learned anything playing this game it's that my brain makes things up.
Pan - I'll take your word on this, and I'll lump it in with Penguin
Penguin - Sure, as you said the Penguin wears a hat. This feels weak IMO
Pumpkin
Server
Story
Sub
Taste
Van
I'd go:
Bowler
Apron
Cotton
Leather
Page
Pan
Penguin
Game
Hole
And yes, I know that's too long a list of backup words