What if all ships can revive, BUT the saved ship will be in a crippled state? ie. 1/4th the power to engines and maneuvering, as well as to rate of fire and module effectiveness.
If an engineer revives, the state of the ship will be at 50% instead of 25%. In the presense of an engineer, if a ship was prior revived by someone else, it will slowly bring them from 25% to 50% while in proximity.
If the revived player so wished, they could use a duplicator to attain 100% effectiveness again.
The revival process should be carefully chosen so as to not be overpowered. It should probably leave the ship in a vulnerable or weakened state during and shortly after bringing someone back.
If duplicator is not used before the end of the match, the player will need to pay for ship repairs, as well.
You have great points, but I don’t agree with “all ships can revive” point. Engi should be the only one who’s able to revive without a duplicator, but others can revive WITH a duplicator. This should make Engi ships more in-demand or whatever. 
Engis are designed to repair so they should do this fully. Other ships should not i think.
I see this like this.
CD: 5 - 10 min.
“Cast” time: Fed engi 2x duplicator revive time, Imp engi 2,5/3x duplicator revive time.
When engi is reviving it lose its shield and energy during that process and revived ship should have 30% of hull hp and 50% of shield and energy so they need to be healed in normal way. Also during reviving engi need to have drones online.
(in free space also engi should have at least 30% of its fuel and during reviving lost it and revived ship should have 25 - 30%)
Now, why its difference between fed and imp cast time.
Fed engi is fast and have less hull hp than imp. With the same cast time fed would have smaller survive chance reviving under enemy fire.
I’d say a 5 minutes cool down is good, maybe less, can be balanced in the future. And I like the idea of the engi losing its shield and energy, so it kind of giving it to the revived ship.