Just a fun thought exercise. Given Picard actually surrendered the Enterprise during the first season of TNG, it is such a classic Picard move to threaten his own resignation in order to try and get Starfleet to restart the Romulan rescue armada construction. But how would the other captains have done it?
Kirk: TOS Kirk would never be presented with a problem of this scope. Movie Kirk would get in a fight with the admirals, storm out, decide to hijack the Enterprise with his old crew and develop some harebrained plan with the slimmest of odds of working out. Surprisingly, Starfleet gives him no more than a slap on the wrist.
Sisko: When he hears 14 worlds are threatening to leave the Federation if they provide aid to the Romulans, he takes the Defiant to one of those worlds and releases radioactive gas into the atmosphere. He then tells the planetary leader "You had a problem helping refugees? No empathy for their condition? Let's see how you deal with being refugees yourself." The other 13 worlds fall in line. Surprisingly Starfleet never reprimands him.
Janeway: Completely agrees with the decision of Starfleet. Returns to her desk and sips coffee.
Archer: Attempts to solve the situation by giving his "gazelle speech" once again. When that doesn't work, he just stands there blinking until the admirals walk out. T'Pol ends up coming up with a reasonable plan that actually works.
Kirk: TOS Kirk would never be presented with a problem of this scope. Movie Kirk would get in a fight with the admirals, storm out, decide to hijack the Enterprise with his old crew and develop some harebrained plan with the slimmest of odds of working out. Surprisingly, Starfleet gives him no more than a slap on the wrist.
Sisko: When he hears 14 worlds are threatening to leave the Federation if they provide aid to the Romulans, he takes the Defiant to one of those worlds and releases radioactive gas into the atmosphere. He then tells the planetary leader "You had a problem helping refugees? No empathy for their condition? Let's see how you deal with being refugees yourself." The other 13 worlds fall in line. Surprisingly Starfleet never reprimands him.
Janeway: Completely agrees with the decision of Starfleet. Returns to her desk and sips coffee.
Archer: Attempts to solve the situation by giving his "gazelle speech" once again. When that doesn't work, he just stands there blinking until the admirals walk out. T'Pol ends up coming up with a reasonable plan that actually works.