State evidence for this 'untyped bonus' thing. You've contended it, but the text does not exist. However, the bonus doesn't need to be 'whitewashed' as the feat directly contradicts the same bonus type rule and therefore supercedes it.
My contention is just the usage of the phrase "enhancement bonus" anywhere you find it in the rules text. I've contended that it takes on the meanings of quantity and type discretely. For example if you look at PHB p 275 it talks about bonuses and penalties at the bottom and, among others, "enhancement bonus" is listed. This is clearly a listing of bonus "types" as if you try to read this some other way it doesn't make sense. On the next page at the top of the right column it talks about modifiers to damage rolls and again listing all the possible types.
The only other uses of Enhancement I've see are the magic item template:
Enhancement: +x (rolls to which it applies such as AC)
and in various feats and items used in various ways (examples):
Subtle Weapon (item) said:
Property: Deal extra damage equal to this weapon's enhancement bonus when attacking with combat advantage.
Obviously untyped due to the "equal to this..." phrasing, but clearly used only as a quantity.
Warding Blade (item) said:
Property: While you wield this weapon in your off hand, you gain an item bonus to AC against opportunity attacks equal to the blade's enhancement bonus.
Also untyped..."equal to..." phrasing and clearly referring to quantity only.
Holy Healer's Weapon (item) said:
Property: Add this weapon's enhancement bonus to the amount healed by your healing word.
Healer's Brooch (item) said:
Property: When you use a power that enables you or an ally to regain hit points, add the Brooch's enhancement bonus to the hit points gained.
Dual Implement Caster (feat) said:
When you use an arcane attack power and you are wielding a magic implement in each hand, you can add the off-hand implement's enhancement bonus to damage rolls.
I was going to say here that it matters which way you read it whether or not the healer's items stack, but in considering it I think they stack either way.
If I'm wrong, then those items are granting an exception to the enhancement stacking rules.
If I'm right, they grant an untyped bonus from different "named game elements" and still stack.
I'm sure you can find hundreds of others but my DDI subscription is currently inactive, so I don't have any good search tools. I just picked a few at random.