Disclaimer: This is all my opinion. Take it with a grain of NaCl.
How and why does an organization with the breadth of FIRST have such a failure like this? The scale of their org, both in terms of scale and volunteer force would make a proper rewrite very easy (if only considering software.)
I personally believe that FIRST needs to take a page out of the book of TBA and rewrite their whole registration system, top to bottom in a high-performing language like C++ or as a module to the "big 2" web servers. Keeping on ASP.NET does them no favors, and the more dependent on the old software they are the messier it'll be when it breaks again (not if.)
Alternatively, can HP or Dell donate some nice servers to FIRST? Sounds like they need more dedicated RAM.
I wish the FIRST team the best of luck moving forward, any system failure on this scale is messy...