I've been spamming Tiger Strikes for the past couple of days and I get a steady stream of blue engrams/items each run (1-2 engram pickups, 2 as rewards at the end or an item and an engram). It takes about a half hour with a decent trio so you're looking at 6-8 blues per hour roughly. I've still never seen a legendary engram drop. My only legendary item is an Unfriendly Giant rocket launcher I was lucky enough to get from a blue engram. All the rest of my weapons and armor are blue rares and I'm stuck at Lvl.24. Bungie really needs to make legendaries more common with you're mid-endgame (23-24) because Lvl.24 is a major bottleneck right now. I mostly play solo so I can't attempt Nightfalls or the harder strikes since there is no matchmaking and Tiger Strikes are easy but don't reward well enough. All I've gotten for my trouble grinding these is a couple of strange coins, a level or two with the Cryptroll, and a ton of blue weapons and armor dismantled.

Honestly the vanguard Tiger strikes is the best and most efficient way to get those. Maybe just try doing those with the vanguard bounties that can apply to strikes to save up time.