Final Edit: Ignore this post. Didn't gain in item level at all due to having an item already of a base of 354 for my base 352.
Just informing Bungie that the Clan Engram I got was an [i]Exotic[/i] 2 (two) levels below my Light Level at reset today (The Dragon's Shadow). It dropped at 354 base (+5) while I was already wearing a 359 and had a total light level of 356. Did not pick up item before reset or even talk to Suraya before getting it (I received it directly into my inventory like was mentioned we should have happen).
Status on Clan Engram: Still broken or broken in another way now.
Edit: To my knowledge (probably wrong, at that) Powerful Engrams drop at a base of your highest item level. This dropped at a base of 354, 2 levels under my average.
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You do realize that the drops are based on your overall light level and not the individual piece right? So in your case you got a drop that didn't help you since your chest piece is higher than the rest of your gear. I believe clan engrams only give you a 1-3 boost over your base level. (in your case 351) It looks like it's working as expected.
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That math doesn't seem to add up. Exotics [i]always[/i] have a +5 legendary mod applied by default, so was it 354 or 359? If your power (as it shows right now) was 356 and the drop was 359, then it dropped higher than your level. So did you really mean it dropped with a total power of 354?