I don't know what the total cost will be as i already had 40% of the parts in my inventory.
I was also buying parts for a Winter Cafe, Winter Red Cottage, Detention Block and other parts for my Winter village at the same time.
All of this cost ~ £700 in total (60% of Barad Dur, the 3 other builds, and general parts to create snow, roads, paths and trees).
At a guess i think it could be done for £600 (maybe less in North America) as long as you substituted all the rare parts, although you will need at least 2 of the 6x6 Cut-Corner Wedge Plate (6106) in dark-bluish gray for one of the upper floors, the lower floors can easily be swapped using a mix of 3x3 corner plates and 3x3 plates.
You will also need a mix of dark gray bricks and plates to strengthen the build in places.
Unfortunately being in the UK means shipping from the USA and Canada is expensive, so it ended up being split across 29 sellers in the EU. It may be half that in North America.
Here is the bricklink wanted list: https://we.tl/QO0f9g8Pi1