Reader print limit of 999

Not sure it will work, but you can specify the number of copies to any value you'd like when printing using a script, like this:

var pp = this.getPrintParams();

pp.NumCopies = 1000;

this.print(pp);

If the issue is the Print dialog then you can avoid it by using this code:

var pp = this.getPrintParams();

pp.NumCopies = 1000;

pp.interactive = pp.constants.interactionLevel.automatic;

this.print(pp);

However, executing this kind of code in Reader is tricky. You could do it using a folder-level script that adds a new menu item or toolbar button, for example, but that would require a more complex set-up.

Use Javascript for this.