Ever since Sherlock Holmes was revealed in Holodeck Adventures, I have spent a lot of time thinking about the possibilities available with his card-drawing mechanism. The first thing that struck me was that it was similar to the "evening up" of Warp Speed. So I set about to design a deck that was similar in play to Warp Speed decks - play as many cards as possible per turn.

Then someone pointed the possibility of Sherlock + Parallax Arguers. Since Parallax Arguers is a "just" response to any action, you can play them as you draw them which will decrease your hand size allowing you to continue drawing until you have no more to play and your hand is up to the size of your opponent's.

Anyway, here is a deck that won a small, local tournament:

Missions:
Corner Enemy Ship
Transport Colonists
Unseat Dictator
Liberation
Salvage Operation
Reinitialize Warp Reaction

Seeds:
Q's Tent
Temporal Micro-Wormhole
Delta Quadrant Spatial Scission
Vidiian Outpost
Hirogen Outpost
War Council
Holoprogram: 221B Baker Street
Obelisk of Masaka
Q the Referee x2

The Sheliak x2
Chula: The Chandra
Friendly Fire
Dead End
Your Galaxy Is Impure x4
Shaka, When The Walls Fell x4
The Clown: Guillotine x3
Kelvan Show of Force x4

Q's Tent:
Hirogen Hunt
Vidiian Sodality
Space-Time Portal
Masaka Transformations
Sherlock Holmes
John Watson
Madam Pulaski
Rituals of the Hunt
Quantum Slipstream Drive
The Pendari Champion
Vidiian Harvester
Hirogen Talon
Alien Parasites

Draw Deck:
Netek x3
Idrin x3
Karr x3
Gann x2
Decaren

Motura x3
Dereth x3
Thaden x2
Science PADD

Icheb x3
Penk x3
Tanis x3
Mabus

Borg Nanoprobes
Olarra
Venatic Hunter x2
U.S.S. Dauntless

Parallax Arguers x8
Dixon Hill's Business Card x2
Revolving Door x4
Memory Wipe x2
Genetronic Replicator
Klim Dokachin

Fair Play
Operate Wormhole Relays
The Big Picture
Reactor Overload
Temporal Vortex
Mirror Image
It's Only A Game

Notes on play:
You have three sources of free plays per turn (Hirogen Hunt, Vidiian Sodality, and War Council) plus your normal card play, plus possible plays from Delta Quadrant Spatial Scission. This should be good to get your hand size down. And Dixon Hill's Business Card and Revolving Door will hopefully help to keep your opponent's hand size up.

On your first turn, hopefully you will have a ship or a Referee card in hand that you can recycle to download a ship so that you can start attempting missions on the first turn. You will probably also want to use your end of turn draw to download a ship to keep your hand size down.

As for dilemmas, I went with Sheliaks because the Revolving Doors can close an opponent's AU Door/Space-Time Portal so he can't get out a Temporal Vortex (Distortion of Space/Time Continuums might also be warranted). And I also went with Diplomacy denial for the non-planets, but you can choose whatever dilemmas you think work best (perhaps some Borg Ships).