Can oembed act as the public endpoint for its own site?

I'm trying to make my installation provide oembed data for its own nodes (paste a node URL into slack or twitter, have it expand into a preview). I'm not interested in displaying outside previews within my nodes. However, I am encountering a cascade of issues that seem to make this impossible.

1. Devel module reports error: Notice: Undefined variable: data in _oembedprovider_handle_request() (line 43 of /var/www/projects/sites/all/modules/oembed/oembedprovider/oembedprovider.inc)., however this is sporadic and I cannot reliably duplicate it.
2. The default location for the oembed provider (according to http://oembed.com/ anyway) should be /services/oembed but it seems to be oembed/endpoint in this installation.
3. It doesn't seem that a consumer could find this location because I don't see any discovery (http://oembed.com/#section4). When I paste a URL to one of my nodes in a slack channel, I do see a hit to that node come in from a slack IP address in the Apache log, so it would appear that they are checking for a link to the oembed URL.
4. If a consumer could find it, it does not seem capable of presenting a response to a query. http://myhost.domain.com/oembed/endpoint?url=http%3A//myhost.domain.com/... returns:
{"type":"rich","version":"1.0","provider_name":"myhost.domain.com","width":0,"height":0,"title":"Could not find a provider that supports this URL.","error":1}
This message makes it sound like it queried a list of other providers and asked for a response for a URL that it serves itself, rather than just replying with the oembed content for its own node.
5. The public endpoint tab in the configuration has no options - is this correct?

Has anyone been able to install the module and have it start serving oembed requests for nodes hosted on that same Drupal installation? Am I misconfiguring something?