By now I'd say it's quite clear that anyone who bet their house on the HTC EVO 3D being released in early June, specifically between the 3rd and 6th, will be homeless soon. With next week's Radio Shack ad (valid from the 5th to the 11th) only showing that the phone can be preordered, it's unlikely that it will available for purchase in mid-June either.
The big day being counted on now seems to fall within the June 24th to 26th range, though I've also heard a few mentions of July 1st.
I have a complete copy of the supervisor's edition of Sprint's playbook dated May 27th here and as you can see above, there's a mandatory training and communication about the device (and the EVO View) on June 18th. The playbook also mentions week 4 of EVO 3D training—see image below—and I've been told that network blackouts are expected from June 28th to July 8th, where no updates will be pushed to any of Sprint's systems; the last time blackouts like this occured was reportedly during the EVO 4G's launch last year.
I've also heard from someone who works at a printing company today who says the Sprint Account Manager there has been told that all EVO 3D retail signage is due by the 24th, with an expected launch date of the 26th.
Sprint is also sending out new email promos about the phone today (shown above) and has released a press release about all of the "exciting content" that will be preloaded.
In other words, let's just say we're closer to the EVO 3D release today than we were yesterday. And while it's not coming this week, all signs seem to be pointing to late June/early July.
Thanks, ArmyAdams, jaydeeIL, Robbie, and Vern G!