When you run the query via your application, what does it return now (as you said you aren't getting 401 responses any longer)? Have you tried querying
http://[wowza-ip-address]:1935 and, if so, what does it return (should return wowza version string)?
This would suggest the application is faulty here if the direct url (in the browser) initiates the recording and this doesn't. The fact that it gives you back the Wowza version html page would also suggest it isn't even hitting the livestreamrecord http provider (as the com.wowza.wms.http.HTTPServerVersion module returns this value).
As a test for your c# application, you could set the AuthenticationMethod to "none" in the livestreamrecord HTTP Provider and see if you are able to have any further luck (ensure you *only* do this on a test environment as it will remove security from the livestreamrecord provider).
In my tests, I think one way you could handle it for test purposes, is to set AllowAutoRedirect to false as there is a 302 redirect (or handle the redirect appropriately). Something like the following as an example: