The best we can hope for in that situation is that enough of the electors are for the project that it becomes too ruinously expensive for Ulthuan. But don't underestimate the depth of Ulthuan's coffers. Two elector counts that they would definitely have to bribe are Boris and Roswita. Boris because having the Eonir on good terms is very good for him. But Ulthuan likely also wants the Eonir on side, so they probably have a suitably large bribe for that... And Roswita, because having the knowledge as the Empire is very good. "Where was Ulthuan when Sylvania was flooded with dhar?" Idk about the rest of the counts.
The Ar-Ulric also has a vote, right? So that's three for us, one against (Nordland).
The Cult of Sigmar (3 votes) might be inclined to oppose it because of the Nordland-Middenland issue, but if there's anything that could make them reconsider is the official support of two Dwarf Kings (Belegar and Kazador) plus a Master Runelord showing up in person to tell them that, hey, this is actually important.
On everyone else, consider the following:
On one side, Ulthuan, who fought against the Empire not long ago and continually supports a rogue province.
On the other, Kislev, one of the Empire's best allies, and the Dwarves, who are
The Empire's ancestral allies and which the Sigmarites are very friendly towards because their religion tells them to.
And, in the end, the only one we need to convince is the Emperor, because Article 1 states that the Emperor (Luitpold) explicitly overrules the Supreme Patriarch (Teclis, hipothetically)