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Setting the server to treat .asp pages as php would IMO be your best option, this means no page url's would change and the .asp extension would be handled like any .php page.
Assuming you are going to be on an Apache server the change could be set up using nothing more that your htaccess file at doc root...
AddType application/x-httpd-php asp
In a newer perspective though, you can Rewrite the URLs and
route it wherever you want. I have used both methods and
this one is more efficient for coding.
On the other hand, it adds to a webmaster's worries, and I suppose they think that can't be all bad. FUD.
You would imagine that a company that claims to be so clever could easily decide if a simple page extension change were just a tech thing or if the content had changed between the two files. I often doubt google's practical intelligence.
They're actually following Internet protocol and web standards, which I believe is a good thing, even if it gives you something else to worry about. The 'pages' (URI) are not the same and should not be treated as the same according to Internet protocol or web standards, and when someone places a link to example.com/some_dir/some_page.net that's where the link goes... Neither Google (nor any search engine) IMO should not arbitrarily attempt to find the 'new location' for the information and then count it as a link or the 'same page', because it's not and anyone who clicks on the link will receive a 404 error, unless there is a redirect in place, in which case, if done properly and through a single redirect to the correct location will be counted properly as a link and the 'new location' by G.