I haven't found anynone who has solved this publicly and in a standard way. Yes, as mentioned, one could fall back to Basic but that doesn't work for authentication schemes which involve requesting a username and password from a CGI form where, as far as the browser sees things, you're falling back to no authentication if Negotiate fails. Maybe that is suggestive that the authentication scheme is broken? I don't know.
I'll tell you what I know, first. Our site is, effectively, Cosign-protected, so we have a similar problem to you: only specially-configured machines respond to the WWW-Authenticate header, so by default we must send all users to our Cosign login page. The trick is that the Cosign server also allows authenticated GSSAPI/Kerberos hosts to complete the authentication process without entering login details, but only on certain browsers, by means of a workaround.
This workaround consists simply of a block of JavaScript within the login page which attempts a HEAD of an SPNEGO-protected resource; if successful, the script redirects the browser to an SPNEGO-protected version of the same page, which grants appropriate Cosign cookies and completes the process without password entry. If the browser lacks any one of JavaScript, Kerberos support or adequate credentials, then the user will see the cosign login page as usual.
So, the above alone might count as an answer to your question; personally though I don't think this goes far enough and what follows is more of a discussion...
The above seems unsatisfactory as it insists that any connecting user agent supports either JavaScript (unlikely to be the case for text-based browsers and HTTP client libraries) or knowledge of the arbitrary path to which we redirect Kerberos-capable users (useless to anything which has not been hard-coded for our site). I've come to the conclusion that there might be a better workaround, or if not, a gap where a standard should be. The best practical suggestion I have is this:
A normal part of the SPNEGO process is that the client attempt to retrieve a page whose initial response is an HTTP 401 but with the header WWW-Authenticate: Negotiate. This is the cue for a GSSAPI/Kerberised client to respond appropriately; a "regular" client will simply display the error page. Perhaps the solution is simply to modify the Cosign server to deliver the human-friendly login page as part of this error response?
It might be technically difficult with off-the-shelf Apache and modules, and might go against various standards (or at least principles). I'm no expert on the systems involved, so can only speculate unless (or until) I get a chance to try it out...
