I was having the same issue with the arcstrider melee not counting toward this. I switched to the gunslinger and found out that the throwing knife kills do count. I use the bottom tree to get the quick recharge.
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I'll give it a try, were you using the bottom Dodge as well? The one that instantly refreshes the melee cooldown? If it does work, I'll probably throw on the Exotic that gives you 2 per charge... Unless you have to have a full set on, of course...