Question

I realize this is a shot in the dark and not the best practice or way of going about it, but I want to do specific logging information as the exception is thrown. It is important that the state of the web form does not change.

Answer 1

You can use 

    try
    {

    }
    catch(Exception ex)
    {
      //your treatment does not contain throw ex.
      //mute exception in order to not change state
    }

You can use this in your webform or in your gloabl.asax in Application_Error (in order to centralize exception treatment)