Pay a fine (1-10mill per a system)
Capture it though glorious battle (short capture times, less then 1 hour timers)
Capture it though more strategic,(rather then brute force), Game play.
Other (Specific below)
First of all, such a mechanic would require a separate game - a mirror of the shard - or some sort of overlay folks could switch back and forth between that would not affect the majority of the players...unless it was set up with a specific sector where such battles took place.
Then you also run into the issue of the Federation not conquering planets - but perhaps liberating them, doing the diplomatic thing, etc, etc, etc. Then again, there's nothing stopping the KDF from going that route as well as outright conquering them. Then you have to consider how the Romulans would feel about any such endeavors, whether they were KDF or Fed aligned.
All in all, you'd have far more questions that would need to be addressed before you got into any of the mechanics of it...literally, before you could design the mechanics, you'd need to answer all sorts of questions.