How to register an AppleScript as a potential default web browser?
Have you tried adding the CFBundleURLTypes and the sub-key LSIsAppleDefaultForScheme?

&lt;key&gt;CFBundleURLTypes&lt;/key&gt;
&lt;array&gt;
    &lt;dict&gt;
        &lt;key&gt;CFBundleURLName&lt;/key&gt;
        &lt;string&gt;Web site URL&lt;/string&gt;
        &lt;key&gt;CFBundleURLSchemes&lt;/key&gt;
        &lt;array&gt;
            &lt;string&gt;http&lt;/string&gt;
            &lt;string&gt;https&lt;/string&gt;
        &lt;/array&gt;
        &lt;key&gt;LSIsAppleDefaultForScheme&lt;/key&gt;
        &lt;true/&gt;
    &lt;/dict&gt;
&lt;/array&gt;


Not sure that it will help, but I have noticed these keys in the info.plist of all the apps that I have checked that show up in that browser list.