Hi!
At this time we do not provide shortcodes to facilitate this, but we’d certainly welcome any feature requests you might post (or add your support to a suitable existing request).
The general approach you are using (soesit) isn’t wrong, but you would additionally need to take care of enqueuing all of the assets that view depends upon – so, at this time, we deem this as an advanced customization that we can’t offer a lot of support for.
An alternative approach you could investigate is using, embedding and if necessary customizing the output of our calendar widget.
Does that help?