Not to sound skeptical, but it sure looks like another case of speculating and profiteering that we've seen happen in plenty of other industries when things like this happen.
First, as already mentioned, although the "direct hit" is not that big, the "indirect hit" is much bigger (motors, heads, etc.) and we really are looking at losing about half of the HDD production.
Second, the amount that prices will go up by for a certain drop in supply is not linear. It depends a lot on the elasticity of the demand. A great example would be oil. Demand for oil is very inelastic. So a doubling of oil prices will not result in a halving of oil demand (and we know that from experience). You'll have to raise oil prices by a LOT to cause a significant drop in consumption.
The problem is HDD demand is inherently inelastic (not as much as oil, of course). The direct retail market (Newegg, Best Buy, etc.) is probably fairly elastic. But most of the HDDs don't go to Newegg; they get shipped to places like Dell. For computer makers, a doubling of HDD prices will probably result only in, say, 10% increase in the price of their product; the fact that people only indirectly buy HDDs as a part of a larger system naturally makes it inelastic.
Also, this inelasticity increases with the deepness of production cuts. If gas prices double, you probably won't mind cutting back on weekend fishing trips, but it would take a lot more than a doubling of gas prices to get you to stop doing something essential, like getting to work. The deeper the cuts in supply, the harder it is to find demand that's "expendable".
In the end, prices will have to increase enough to squelch demand by almost half, and frankly, given these circumstances, I'm expecting a lot more than a mere doubling or even tripling of prices.