custom webdav implementation in IIS, gives 405 on PROPFIND - iis

Question

I have created a custom webdav implementation with a HttpHandler, to serve files in a database via webdav protocol to a client.
On Cassini, my VS Development server I can access this without problems.
Now I am trying to debug this site in IIS, and that doesn't work.
I have the IIS 7.5 Webdav module uninstalled.
Some snippets of my web.config:
<system.web>
...
<httphandlers>
<add type="Test.WebDAVHandler, Test" verb="*" path="*"></add>
</httphandlers>
...
</system.web>
<system.webserver>
<modules runAllManagedModulesForAllRequests="true">
<remove name="WebDAVModule">
</remove>
</modules>
<validation validateIntegratedModeConfiguration="true">
<defaultdocument enabled="true">
<files>
<add value="example.aspx"></add>
</files>
</defaultdocument>
<handlers accessPolicy="Read,Write,Execute,Script">
<remove name="WebDAV">
<add name=".NET Runtime" verb="*" path="*" preCondition="classicMode,runtimeVersionv2.0,bitness64" requireAccess="None" resourceType="Unspecified" scriptProcessor="C:\Windows\Microsoft.NET\Framework64\v2.0.50727\aspnet_isapi.dll" modules="IsapiModule">
</add>
</handlers>
</validation>
</system.webserver>
When I connect to this site by using the Map network drive option of Windows 7 and inspect the requests using Fiddler, I see that the after some authentication, the client does the following request:
OPTIONS localhost/explorer and gets the following (shortened) response.
HTTP/1.1 200 OK
Allow: OPTIONS, TRACE, GET, HEAD, POST
I am missing some allowed verbs here, like PROPFIND.
The next request the client does is a PROPFIND.
The server responds with a 405 Method not allowed.
I looked at the request tracing, and the DefaultDocumentModule is causing this error.
When I disable this module, the DirectoryListingModule causes this 405.
Does anyone have a clue how to fix this, so that I can use webdav with my custom handler?