I think you are attacking it from the wrong angle by trying to encode all posted data.
Note that a "<" could also come from other outside sources, like a database field, a configuration, a file, a feed and so on.
Furthermore, "<" is not inherently dangerous. It's only dangerous in a specific context: when writing strings that haven't been encoded to HTML output (because of XSS).
In other contexts different sub-strings are dangerous, for example, if you write an user-provided URL into a link, the sub-string "javascript:" may be dangerous. The single quote character on the other hand is dangerous when interpolating strings in SQL queries, but perfectly safe if it is a part of a name submitted from a form or read from a database field.
The bottom line is: you can't filter random input for dangerous characters, because any character may be dangerous under the right circumstances. You should encode at the point where some specific characters may become dangerous because they cross into a different sub-language where they have special meaning. When you write a string to HTML, you should encode characters that have special meaning in HTML, using Server.HtmlEncode. If you pass a string to a dynamic SQL statement, you should encode different characters (or better, let the framework do it for you by using prepared statements or the like)..
When you are sure you HTML-encode everywhere you pass strings to HTML, then set ValidateRequest="false" in the <%@ Page ... %> directive in your .aspx file(s).
In .NET 4 you may need to do a little more. Sometimes it's necessary to also add <httpRuntime requestValidationMode="2.0" /> to web.config (reference).
eval() is not necessary. This will work fine:
var date = new Date(parseInt(jsonDate.substr(6)));
The substr() function takes out the /Date( part, and the parseInt() function gets the integer and ignores the )/ at the end. The resulting number is passed into the Date constructor.
I have intentionally left out the radix (the 2nd argument to parseInt); see my comment below.
Also, I completely agree with Rory's comment: ISO-8601 dates are preferred over this old format - so this format generally shouldn't be used for new development.
For ISO-8601 formatted JSON dates, just pass the string into the Date constructor:
var date = new Date(jsonDate); //no ugly parsing needed; full timezone support
Best Answer
You can start export as a background task.
In the meantime you will be checking the status of the operation and displaying some animation to the user saying "Your export is in progress, please wait.".
When the export is complete you will update that portion of the page using Ajax and display a message to the user: "You can now access your exported file at this link. It will be there for you during the next 24 hours.".