I still don't understand how a Reach weapon would keep anyone "at bay." Are you perhaps confusing Reach with Threatening Reach?The purpose of the Reach weapon is to keep non-OoE foes away from the Avenger, so he can get full utility of hie OoE, right?
If Reach weapons cannot strike adjacent targets (I don't know- haven't even looked at the Reach rules since I'm playing a Warlock), then a Reach-weapon equipped Avenger needs a way to deal damage up close while still using the Reach weapon to keep others at bay. Monk's FoB would seem to be an answer: either unarmed or with the Reach weapon, Monk attacks generally ignore weapon properties, so a Monk FoB attack with a reach weapon would still work close in.
All a Reach weapon does is let you attack something 2 squares away, in addition to being able to attack something adjacent to you. That's it.
Also, as others said, Monk's Flurry of Blows is auto-damage. Melee or implement doesn't factor into it at all. If you hit with an attack on your turn, then you can use FoB to deal damage to a creature adjacent to you. And even if Reach weapons prevented you from attacking adjacent targets (just to be clear: they don't) then FoB still wouldn't be 'the answer' for Avengers. With a monk multiclass, you can only do FoB once per encounter. And you still need to hit with an attack first before you can trigger it.