You don't need a lot of Voyager to win. Games do not always last 4 turns or less. I hate to break your bubble, but here's a non-voyager deck that wins.

Here's an End Transmission Deck I've been working on for a while. It relies on the mirror ore processing along with a variety of other card drawing mechanisms to make sure you have an end transmission every turn.

The Wrong Doors, along with the STPs and AU doors make sure your Q-flash stays open (far more important than any other doorway.)

You will tend to find that the combos presented here are very hard to get through without triggering friendly fire.

Once the friendly fires are running, don't be afraid to ops download every turn-- it's not like you're loosing card draws!

One of the various nice things about this deck is that if you park Leeta at Ops, if someone tries to kill her so they can commandeer the station, you can drop a DH and download your deck.

Missions:
Disrupt Alliance
Search for Rebels
Pegasus Search
Reported Activity
Mine Dilithium
Halkan Council

Counted Seeds:
Q The Referee x2
Quark's Isolinear Rods
Sisko 947 subroutine
Space Time Portal x2
Alternate Universe Door
Terran Rebellion HQ
Mirror Terok Nor
Bajoran Wormhole: Mirror Universe
Mirror Image
Defend Homeworld
Dead End
Q's Tent
Q-Flash (as side deck)
Q-Flash x5 (as Dilemmas)
Chula: The Chandra x5
Friendly Fire x5

Sites:
Mirror Ops
Docking Ports
Science Lab
Ore Processing Unit
Promenade Shops
Infirmary

Q-Flash:
Hide and Seek x 3
Fighting Words x 2
Penalty Box x 3
Mandarin Bailiff x 2
Q-Type Android x 3
I Tried to Warn You
Q's Planet

Q's Tent:
Classic Medical Tricorder
Classic Communicator
Mirror Dagger
Medical Kit
Klingon Disruptor
Process Ore
Ezri
Operate Wormhole Relays
Defend Homeworld
Temporal Vortex
Vulcan Mindmeld
Classic Type 2 Phaser.
Classic Tricorder

Draw Deck:
Kivas Fajo: Collector x 12
End Transmission x 20
Bajoran Wormhole x 2
Senior Staff Meeting x 2
The Art of Diplomacy x 2
Emblem of the Alliance
Emblem of the Empire
Palor Toff x 10
Countermanda x 3
Mutation x 8
Power x 6
Wrong Door x 10
I'm a Doctor Not a Bricklayer
ISS Enterprise
Scorched Hand
Oof!
Villagers with torches
AU door x 2
Regenerate
Colony
Defiant
Rebel Interceptor x 2
Mirror Defiant
Mr.Rom
Mr Sisko
Mr.Quark
Mr.Nog
Mr.Brunt
Starfleet type 2 phaser X 2
Federation PADD x 2
Commander Leeta
Professor Sisko
Fontaine
Transporter Chief Kyle
Marlena Moreau
Chief Surgeon McCoy
Captain Dax
Captain Bashir
Security Chief Sulu
Chief Navigator Chekov
Comm Officer Uhura
Smiley
Chief Engineer Scott
Mr.Tuvok
First Officer Spock