Strictly speaking, probably find a new officer - I think everyone else is comfortably set in their positions on the Enterprise proper, and, given the difficulty he had in the immediate post-Nemesis restructuring, I think he learned well that he can't just recreate the magic of the original crew of the Enterprise under his command. If Picard needs a new first officer, while he might have faith in his crew, he'd also take into account if any of them want or are ready for the position - of the options, La Forge HAD the opportunity to become a first officer, offered to him by Riker first off when he accepted command of Titan, even WAS a captain for a brief period, and came to the conclusion that he preferred being Chief Engineer, that he did his best work there, and it's likely a similar scenario for Crusher (plus Starfleet Command would probably raise several eyebrows at the idea of Picard's first officer being his wife). So I think that immediately puts both of them out of the running. They have their positions that they love and don't need to move outside of those particular roles - they're where they do the most good and have the most fulfillment right now, why change for the sake of keeping matters of promotion "in-house"?
So dropping down to Konya, Trys, or Elfiki... I think Konya would move into the Security Chief position that Smrhova has left sooner than first officer, given his position as a deputy security chief, and Trys is not ready for the position (though if you gave her another five to ten years and ask again, I'd probably be willing to change my mind). As for Elfiki... She's a "maybe" in my book, but I lean more towards her not wanting the position. Granted, there's not a lot of development for her, but she seems to be good as a science officer, and wouldn't necessarily seek out the transfer to command that would come with that particular promotion.
So I think that Picard's search would come down to having to bring in someone new. And, honestly, I'm not all that on board with the concept of "cannibalizing" from other lines - it's a bit too "small universe" for me to just trade around the same core group of characters in an organization like Starfleet, which has hundreds (if not thousands) of starships and starbases across even just the Alpha Quadrant alone. Plus it offers the opportunity for new avenues of exploration, by potentially bringing in some undeveloped species or characterization that hasn't been covered in depth.