Janeway's choice seemed like horribly failed diplomacy and greed. Such a simple solution existed if they just let the ship go, this Spatial Trajector could absolutely have helped the crew. Why didn't the crew themselves take the Spatial Trajector shortcut?
JANEWAY: What do you think? Would it be possible to modify your technology so we could use it?
EUDORA: I tried to tell him.
JANEWAY: What is it?
GATH: We cannot share our technology. Once it's out of our control, it might fall into the hands of those who would abuse it, and our canon of laws strictly forbids that.
KIM: But we wouldn't abuse it. Don't you see what it would mean to us?
With good diplomacy they had two ways the Trajector could have greatly benefitted them, and of course, plan C which is to not use it at all:
These plans are as follows, and detailed a bit further down:
A. STSGMH (Screw The Ship, Get Me Home) 5-year plan (estimate).
B. IWMPST (I Want My Pretty Ship Too) - 40-year plan (estimate).
C. STCSMS (Screw The Crew, Save My Ship) - 70-year plan (the one they chose)
As Gath said Sikaris' space-folding technology was protected by laws. They were afraid Trajector technology would be abused if they lost control of it. So they wrote their laws to prevent anyone else from making another Spatial Trajector. OK, great! They can KEEP control. They can keep everything! Just get the crew home in two simple steps!
First, Chakotay already confirmed that the Spatial Trajector matrix could be reconfigured to work on a distant planet:
KIM I can't believe they're not going to help us.
TORRES Some kind of hospitality. 40,000 light years. Even if that's as far as we could go, it would still knock about four decades off our trip.
CHAKOTAY And the possibility exists that we could reconfigure the matrix at that point, to take us another 30,000 light-years, right into Federation space.
At this point Tuvok kills the logic train saying "They have already said no." Here they seem to get hung up on moving Voyager and forget the actual mission of getting the crew home.
Possible ways home:
Plan A is a very simple two-hop plan which saves 65 years of risky space travel. It assumes Chakotay was correct and the Sikarian laws are what they claim to be - technology security. Janeway uses diplomacy to get Sikaris to build a Spatial Trajector on the Midway Planet - with no help from Voyager (respect their laws). The crew hops to Midway, then home. Sikaris can keep the new device or destroy it - they still own it. Voyager buys this labor with their valuable stories. Let's assume building a Trajector takes 5 years (blind guess), but certainly much less than 70. Sikaris gets exactly what they want, no laws are broken, no-one steals their technology, the crew is home.
Plan B is an option to just move Voyager 40,000 light years through the Trajector, piece by piece. This considers the possibility that the Sikarian laws were protecting nothing at all, Chakotay doesn't know what he's talking about, and it's somehow impossible to replicate a Trajector. Fine. Some comments suggest this, that Chakotay had no clue what he was talking about re: the claim that the matrix could be reconfigured. If the Trajector can't be copied, the ship most defiitely can be. Maybe it takes 10 years to dismantle Voyager and rebuild her on Midway Planet. Launch the rebuilt Voyager from Midway Planet and get home 30 years earlier than driving the whole way. Sikaris gets what they want, no one steals their tech, no laws are broken, the crew AND Voyager are home. Resources? Sikaris can jump to any system within 40k LY for free, so they had limitless resources to build a new ship.
Plan C was Tuvok's plan - this assumes the Sikarians don't understand their own technology, Chakotay was wrong about reconfiguring the matrix on another planet, and also Torres misspoke when she said the Trajector was incompatible with Federation technology:
TORRES This will never be compatible with Federation technology.
So for this plan we must assume she meant to say the Trajector can't work anywhere but Sikaris and just misspoke her line.
Tuvok's plan was to steal the technology, jury-rig it into a Federation starship, haphazardly rush into a shade-tree garage engine rebuild (causing them to forget about antineutrinos), and anger the Sikarians. After those steps permanently close the door to Sikaris, drive home for 70 years and hope your grandchildren see Earth.
Now I can't even imagine why they didn't consider copying the trajector or rebuilding the ship at the midpoint. No one mentioned it. They seemed obsessed with getting their ship home and never even mentioned the crew.
This is only a problem because on another time, they WERE willing to leave the ship behind. In Eye of The Needle they were ready to beam themselves through a wormhole onto a Romulan research ship. Of course, it took them 20 years into the past so it was a no-go.
Remember they had extremely generous offers for both resources and labor. Building another small personal trajector should be simple. Rebuilding Voyager - a little more challenging but much better than plan C.