1 option you might not have considered though its a bit clunky and not a nice solution at all, anyway here goes...
Assuming your web servers have tps logging for error's enabled, and that you either have calculations which fail but in such a way that it doesn't impact your performance 
If you have the space on the web servers, let these files build up for a reasonable period, then use a powersheel script or vb script to read the file names and dump them into a csv with.
The tps logging files for the users get a new 1 created each day, so this gives a rather clunky method to get a list of logins and the date they logged in.