So, Tuvok directly states that he will need several hours. Let's assume several equals more than three. The Caretaker is intent on stranding them there with his self destruct, so Banjo Man will be no help.TUVOK: Captain, I can access the system to send us back to Federation space, but it will take several hours to activate.
JANEWAY: Unless you help us.
CARETAKER: Oh, I wish I could but I have very little time left, so I have initiated a self-destruct programme.
JANEWAY: If you destroy the Array, we'll have no way to get home.
CARETAKER: The Ocampa's enemies can not be allowed to control this installation. In minutes, it'll be destroyed. You have to go. Go now.
(The Kazon ship hits the Array. The holographic barn turns into the high-tech room. There is a giant purple blob at one end.)
TUVOK: The Caretaker?
JANEWAY: Voyager, report.
PARIS [OC]: Kazon vessel
[Bridge]
PARIS: Just collided with the array, Captain. Are you all right?
JANEWAY [OC]: Affirmative.
Banjo-Man dies, and the self destruct is out of play.[Array]
JANEWAY: Stand by.
CARETAKER: The self-destruct programme has been damaged. Now this installation will not be destroyed. But it must be. The Kazon must not be allowed to gain control of it. They will annihilate the Ocampa.
(The Caretaker shrinks into a hand-sized rock. Janeway picks it up.) TUVOK: Shall I activate the programme to get us back?
JANEWAY: And what happens to the Ocampa after we're gone?
TUVOK: Captain, any action we take to protect the Ocampa would affect the balance of power in this system. The Prime Directive would seem to apply.
JANEWAY: Would it? We never asked to be involved, Tuvok, but we are. We are.
[Bridge]
Now here's where the choice comes in. Presuming they can get the Kazon to not kill them and they get the necessary few hours to program the array to jump them back to the Alpha Quadrant(presuming that they don't all die in the process, like a third of their crew did on the way to the Ocampa system), the Kazon will have access to the Caretaker array. Whether or not they get home, there's the unfortunate problem of giving the Kazon, a primitive race who only have warp drive because they were uplifted by the Trabe as slaves and then rebelled and took over the ships, even more powerful technology that can yank ships across the galaxy.
Jabin says(he may be bluffing for all we know) that he's bringing in additional forces to fight Voyager and secure the Array, giving them a limited window for this.(Voyager is still taking weapons fire.)
JANEWAY: Mister Tuvok, ready the tricobalt devices.
TUVOK: Aye, Captain.
JANEWAY: Open a channel to the Kazon.
KIM: Channel open.
JABIN [on viewscreen]: Be advised, Captain. I have called for additional ships.
JANEWAY: I'm calling to warn you to move your vessels to a safe distance. I intend to destroy the Array.
JABIN [on viewscreen]: You can't do that!
JANEWAY: I can and I will. End transmission.
KIM: They're increasing fire, Captain. Shields are holding.
JANEWAY: Move us four hundred kilometres from the Array, Mister Paris.
PARIS: Yes, ma'am.
TORRES: What do you think you're doing? That Array is the only way we have to get back home.
JANEWAY: I'm aware everyone has families and loved ones at homes they want to get back to. So do I. But I'm not willing to trade the lives of the Ocampa for our convenience. We'll have to find another way home.
TORRES: What other way home is there? Who is she to be making these decisions for all of us?
CHAKOTAY: She's the Captain.
TUVOK: The tricobalt devices are ready.
PARIS: We're in position.
JANEWAY: Fire.
(Two blue torpedoes strike the Array. Mega-KaBOOM as it falls apart.)
KIM: The lead Kazon ship is hailing us.
JANEWAY: On screen.
JABIN [on viewscreen]: You have made an enemy today.
TUVOK: They are withdrawing, Captain.
Janeway's justification though is that she's protecting the Ocampa. Not protecting the galaxy from Kazon dominion, but protecting the Ocampa.
So, with the Caretaker dead, the station's self destruct blown up, and the Kazon firing at them, they would have to:
A. survive the firefight against the Kazon fleet long enough for the Tuvok to figure out the array and set up the array for the jump home.
B. destroy the Kazon, buying enough time for Tuvok to program the array and jump home, and maybe blow up the array on a timed explosive.
C. convince the Kazon to stop firing, set up the array, jump home, and hope the Kazon make good overlords with their new tech advantage.
D. convince the Kazon to stop firing, set up the array, jump home, and hope the Kazon don't know how to reverse engineer Caretaker technology.
E. convince the Kazon to stop firing, and somehow also convince the Kazon that leaving the Array and the Ocampa alone would be a good idea.
F. go to the Caretaker Array, grab Tuvok and Janeway, take care of Jabin, go to Ocampa, and have a nice bowl of Taco Bell meat while they wait for all of this to blow over.
Or....
G. Blow up the Array, and hope the Kazon don't care that they just denied them a vital resource.
I think their best bet for getting home was option B. But how feasible was Option B, considering how hard the Kazon were fighting them?