Sword & Board and Avenger both have edges so here are brainstorms for monk/champion... not necessarily the vector to take the dedication/edges just some ideas.

Monk Dedication (Zero Edges currently)
Avoid 10
*Makes it take slightly less mana to maintain (might make a Storm giant monk more possible)
Transcend 20
*Improved Modifiers like add + dex or str or hit
Defy 23
*higher chance to impact off the consecrated armor
Respond 25
*high chance to snatch or break weapons
Intensify 30
If you target flees you cease your intensify (stops lag), or perhaps a calm/fluid intensity that doesn't tell your enemy that you have just intensified yourself... (which they flee and wait for it to end).
Ascend 31
*More likely to succeed or less taxing.
Anticipate 35
*Anticipate lasts longer or something.

Champion Dedication (Zero Edges currently)
Bat 10
*Perhaps your primary stat (str, dex, or wis) allows you to do the bat skill that favors your primary stat more often.
Fend 15
*Small chance to give a short lived crippling strike/bleed depending on staff/polearm when you're fending off more than one enemy.
Maneuver 24
*Maneuver might cause a stun/bleed effect (possible to friendlies too if use on a friendly)
* High chance of success
Marshal 31
*Rally has a chance to cutoff target
*Rally lasts longer.
*Phoenix has a small chance to give extra attack on a parry (thinking like porcupine)
*Phoenix lasts longer.
*Forefront - the fury of your charge to the frontline gives pause to the enemy (1 round lag or morale drop, or something
*regroup - got nothing here... Improve chance?

Just some spit balls for you. Thanks for your time and effort.