Barovia exists within a larger demiplane

Since as far back as at least 3rd edition, Barovia has been a location within the Demiplane of Dread, sometimes called Ravenloft. Curse of Strahd mentions this in the sidebar "A Classic Retold":

...Ravenloft, home of the Domains of Dread.

[...]

...The lands of Barovia are from a forgotten world in the D&D multiverse, and this adventure gives glimpses into that world. In time, cursed Barovia was torn from its home world by the Dark Powers and bound in mist as one of the Domains of Dread in the Shadowfell.

You can find more information about Barovia's placement in the Demiplane of Dread within the Ravenloft Campaign Setting – Core Rulebook for 3rd edition which has a section on Barovia beginning on page 112.

This section exists among other descriptions of some of the Domains of Dread that lie within the demiplane.

This chapter describes most of the known domains of Ravenloft. Particular attention is devoted to those domains that might be homelands for Ravenloft PCs. The catalogue that follows is by no means comprehensive. Other domains almost certainly exist, and as the ages roll on, the Land of Mists will no doubt continue to grow like a creeping cancer, spawning new lands brimming with new nightmares.

Barovia is unique in that travel outside of its borders is prevented:

No matter how far a creature travels in the fog, or in which direction it goes, it gets turned around so that it eventually finds itself back in Barovia.

...However, the 3rd edition rulebook mentions travel between the Domains of Dread (albeit with some side-effects of note)

Journeying from one domain of Ravenloft to another — and even within the bounds of a domain — can be a perilous and maddening undertaking. The Land of Mists has its share of physical dangers, including treacherous terrain and waters, inclement weather, and wild predators. These hazards aside, overland travel often involves risks that are subtler, though just as hindering and frightening.

[...]

...Travelers learn quickly that in the embrace of the Mists, time and distance can be meaningless.

There is also mention of Mistways which are routes between the Domains of Dread. Only one of these charted routes connects to Barovia, and knowledge of it among navigators that live in Barovia may have been lost since Barovia has been isolated for so long.

The Bleak Road: Southern Barovia — Northern Vorostokov (Poor Reliability, Two Way).

Aside from that, travel through the mists outside of the chartered Mistways should be possible once Strahd is defeated:

The fog that surrounds the land thins, and it no longer harms those who pass through it...

The Barovians take the sunlight as a sign that the evil in their land has been purged. Though escape is now possible, most Barovians realize that they have nowhere to go and no reason to leave. A few depart, fearing the return of the darkness or longing to see their ancestral homelands. Those who have souls can leave the valley, while those without souls fade into nothingness as they take their first steps beyond the edge of Strahd’s former domain.

...a map of at least part of the Demiplane of Dread can be found in 3rd edition's Ravenloft Campaign Setting – Core Rulebook. It is split into a few parts, but below is an image which combines them (source):

Assuming casting Dispel Magic on the Alarm is infeasible (perhaps the makers of the Vault were so meticulous that they cast Alarm on each individual piece of gold), this seems like an ideal use case for Leomund's Secret Chest

Since you've said the players have several thousands of their own gold outside the contents of the Vault, they could spend 5,050 gp to have the material components for Leomund's Secret Chest commissioned (see spell description below; I presume there's no time pressure until the Alarm is triggered). The wizard may need to research and learn Leomund's Secret Chest, as well (I don't have my books handy at the moment and so can't price out the research needed to learn the spell through experimentation, but it's a minimum of 8 hours and 200 gp to copy it into the spellbook--halved if your wizard is of the conjuration school).

Leomund's Secret Chest
4th level Conjuration
Casting Time: 1 Action
Range: Touch
Components: V, S, M (an exquisite chest, 3 feet by 2 feet by 2 feet, constructed from rare materials worth at least 5,000 gp, and a Tiny replica made from the same materials worth at least 50 gp)
Duration: Instantaneous

You hide a chest, and all its contents, on the Ethereal Plane. You must touch the chest and the miniature replica that serves as a material component for the spell. The chest can contain up to 12 cubic feet of nonliving material (3 feet by 2 feet by 2 feet).

While the chest remains on the Ethereal Plane, you can use an action and touch the replica to recall the chest. It appears in an unoccupied space on the ground within 5 feet of you. You can send the chest back to the Ethereal Plane by using an action and touching both the chest and the replica.

After 60 days, there is a cumulative 5 percent chance per day that the spell’s effect ends. This effect ends if you cast this spell again, if the smaller replica chest is destroyed, or if you choose to end the spell as an action. If the spell ends and the larger chest is on the Ethereal Plane, it is irretrievably lost.

Preparing the Chest for use in the heist

Using these, they can hide the larger chest on the Ethereal Plane with a single casting of Leomund's Secret Chest, linking the full-size and replica chests. This could even be done a day in advance to recover the spell slot. The next day, from inside the Vault and "while the [larger] chest remains on the Etereal Plane, [the wizard] can use an action and touch the replica to recall the [larger] chest. [The larger chest] appears in an unoccupied space on the ground within 5 feet of [the wizard]."

Loading up the loot

From inside the vault, they can load up the coins into the larger chest, which can contain up to 12 cubic feet of nonliving material acccording to the spell description. I used an online calculator to calculate the volume of 10,000 lbs of gold (although admittedly, that's assuming a single, solid mass), and it comes out to 8.29 cubic feet. Assuming the coins are thin cylindrical solids, if the coins are placed in rows or stacks (think like rolls of coins, but without the paper roll), you're looking at a packing factor of about 78.5% for a square (as seen from the end of the row/top of the stack) arrangement, so at most the 12 cubic foot interior of the chest could hold an equivalent of 9.42 cubic feet of gold coins (specific to this particular arrangement of coins, and notably more than the 8.29 cubic feet that much mass of gold would occupy). During this time, the gold is still inside the Vault, and so the Alarm will not trigger. This part is time-consuming, but under no functional time pressure, and all party members can help arrange the coins for tight storage. What's more, if it takes days of labor (which the party seems willing to put in, what with 70 castings of Fabricate involved in their original plan), the party can leave the chest inside the Vault and it'd be so absurdly difficult for someone to get the chest up and out of the existing 2 foot square hole that anyone else who manages to get inside is likely to leave it alone. I've never worked with this many coins, but I still suspect it'll take fewer days than the 70 castings of Fabricate would require.

The great escape

Once the gold is loaded into the larger chest, it can be closed (which isn't technically required, but it's worth doing just in case someone or something comes across it on the Ethereal Plane) and they can "send the chest back to the Ethereal Plane by using an action and touching both the [larger] chest and the replica." At this point, the gold leaves the Vault and the Alarm triggers, but all the party needs to do is go back up the hole (or even Dimension Door out if they're feeling fancy and don't want to be seen leaving the building in which the Vault entrance is hidden) with the Tiny replica and go about their business as though nothing has happened. As long as they recall the chest to the Material Plane within 60 days (by using an action with the Tiny chest), there's no chance of it being irretrievably lost on the Ethereal Plane. What's more, after this entire heist is done and they unload the gold wherever, they can sell off the chest and replica to recoup some of that initial 5,050 gp cost for the materials if they're so inclined.