Stacking AoMF and Body Wrap of Mighty Strikes?

[chaoseffect]

Body Wrap of Mighty Strikes

So if I were using an Amulet of Mighty Fists and a Body Wrap of Mighty Strikes, could I essentially combine them? The actual enhancement to attack would not stack, but what about the weapon properties? For instance if I had a +3 AoMF and a body wrap with +1 Flaming could I activate the body wrap and have +3 Flaming for one attack?

If so it could be a useful way to get around the tight enhancement restriction on an AoMF if you plan on using a weapon ability that can only really trigger once per round anyway, like Conductive or Phase Locking.

[Nefreet]

I'd imagine it would be akin to loading a +1 Flaming Arrow into a +1 Frost Longbow.

The enhancement bonuses wouldn't stack, but you'd benefit from both properties.