Nah, OT doesn't make sense to me. I know this is not popular but a trade down makes more sense to me. For starters, there's a chance you could use the 3rd pick in the draft on an OT and he ends up riding the bench if the other two are healthy. Unless you trade one, but that seems unlikely. And you aren't going to move one to OG either.
Parsons is good but is he so good that I'd turn down a slide down in the draft, pick up an extra two or three that I can use to really overhaul the defense? Throw in the fact with a restricted cap next year and a lot of holes to fill, I might be more inclined to land as many guys as I can in the first 2-3 rounds.