I see where you're coming from, and with the Skins having an extremely limited amount of picks you would expect them to pull th trigger on a deal like that, but there are a few things that might get in the way.
The Skins don't seem to value draft picks like other teams, and especially don't seem to value having a lot of draft picks. They choose to build their team through FA instead of the draft. A team like that will value a high first round pick more than two late first round picks. Add the 24th & 28th overall picks being worth only 1,400 points while the 6th pick overall is worth 1,600 points, and I don't see it happening. Even if the Redskins were willing to swing a trade they would probably want NE's third rounder too, which doesn't make sense (since they don't value draft picks), but they would probably ask for it, anyway. Now If they were willing to take just 24 & 28 for their six round pick maybe I would do it, but probably not. I like Landry a lot and think he is the best Safety in this draft, but I am not sure I would give up two first rounders, and the contract a 6th overall draftee receives. NE's two late first should actually combine for a smaller contract than Landry by himself, so NE would also loose cap space and not just two first rounders. So, again I probably wouldn't do it.
Trading 24 & 28 for 16 and 47 is much more reasonable because of this. You would spend more on the 16th overall pick than 24, but the 16th overall pick can be signed to a 6 year contract while 24 can only be signed to a 5 year deal. The 47th pick can only be signed to a 4 year contract, but would cost less to sign than the 28th overall pick, and some of the same talent could be available at 47.