Since OP mentioned longshots, I went through the bargain bin and pulled one from each category who can be had cheap and could realistically land in the top two tiers of fantasy scoring. Keep in mind these are longshots before you blast me for even bringing up the names.
WR: Jermaine Kearse - Dude catches everything thrown his way, even when contested or being interfered with as you can see here:
https://www.youtube.com/watch?v=7b1Dc03OEfU
May never reach full potential in that offense, but I think there is much more to him than just deep ball specialist.
TE: Ryan Griffin - Another guy who has a ton of potential and is in an offense, where he could rise in the next year or two. I think he is the best TE on a team where Owen Daniels produced for years. I think he can be better. Of course he will need a QB for that to happen, but I'm buying.