Hand in Hand vs. Hand in Glove

This is a dabate i am having with a collegue at work. We are trying to figure out under what circumstances to use each one of these two similar idioms.

My understanding is:

Hand in Hand:
When A is naturally/axiomatically coincidental with B. e.g. statement of fact: Fire and smoke go hand in hand. e.g. to argue a relationship as fact: Greed and fraud go hand and hand.
Or when A and B are working together closely to achieve a common goal: The employees worked hand in hand throughout the night to finish the project.

(Fits) Hand in Glove: When activity A is pursued specifically/intentionally to enable/cause consequence B, typically for a sinister purpose. E.g. to argue intention/motive: His desire to for power fits hand in glove with his desire for retribution.

However, I often see hand in glove being used describe when one party in working complementary with another to achieve the same objective. To me, hand in hand, would be more appropriate. Thoughts?

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I and the dictionaries generally agree, though I doubt any of us take such a specific view as yours:

Hand in hand: in close association; together; closely associated; concurrently; conjointly

Hand in/and glove: very intimately associated; in extremely close relationship or agreement

H in G just seems to be an extreme form of H in H. I have no doubt, however, that many native speakers mix them cavalierly.
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