Less than a week for 3.35 and Deep Dungeon, who wants to bet that it won't last more than one or two weeks, people get their glowy weapon, then go show off in cities and won't touch DD again.
I'll take that bet.

Deep Dungeons will be highly popular with the non-hardcore playerbase, and that's a huge portion of the playerbase. I intend to use it not just for building a new weapon, but for leveling other jobs without having to lean so heavily on FATEs and traditional dungeons.

Also, you're forgetting the bane of your own existence... lockouts!

There's no way in Eorzea you'll get that capped-out weapon finished in two weeks. Though if you have no need for another high iLevel-weapon, then yes, I suppose you could get a glamor piece (maybe?) in a couple weeks. But most people I know will be going for the built-out weapon, not glamor.