There is no doubt that different mining techniques (here is a list of some of the types with descriptions and animation http://www.bcminerals.ca/pdf/underground_mining_methods.pdf) are more expensive then open pit mining. However when they talk about the cost of DEEP mining they are talking about the cost of supporting that mining method. The mining method itself is dictated by the geometry of the ore body, rock type, technical issues (rock stability/integrity, brittleness etc), grades etc.
The additional costs of DEEP mining have to do with moving ventilation (heat and air up/down), pumping water (most mines in the Canadian Shield battle water problems), haulage to surface (men, material, and ore), supporting the integrity of the mining workings (bolting, screening, grouting, bracing, etc). You need bigger pumps to get the lift to surface, bigger ventilation systems to handle the decrease in efficiency associated with drag and pressures, longer times for switch over of the shaft/cage from hauling people to hauling ore, longer cycle times from surface to depth, more emphasis on mine ability to handle the rock stresses/pressures at depth.
When all is said and done the deeper you go the more expensive it get to operate. Whether you go deep is dictated by the value contained in the ore. A 2500m mine would certainly be considered a deep mine but well within the realm of current technology in mining.
As to the apparent shape of the Eagles nest, a compact vertically stacked ore body is far cheaper to mine then the same amount of ore spread out laterally and to depth.
... Been There
