Am I missing some internal trigger for it? I've done every other quest on the island...and Neloth has given my character the Heart Stones and Azra's Staff quests fifty times already.I've tried reloading saves from before entering Tel Mithrayn and even redoing the entire Dragonborn expansion from scratch.Twice.And he still gives me nothing but 'I'm running low on Heart stones' or 'Perhaps later, you see I'm a collector of staves'...really starting to irritate me.In six weeks of playing DB I've never seen the Telvanni Research quest

Have you helped his assistant?

Yep.I helped his assistant with the rogue Ash Guardian.