The latest experimental build has Steam Workshop support added for Custom Maps!
You can use the level editor to upload to steam workshop in the new Workshop Window.
Create a level and use the Export Window to export a level bundle. Then use the workshop window to create a new workshop item, select the bundle to use and set the name / description / etc and Submit Item to upload it.
If you are subscribed to any workshop items, it will find them on startup and they should just be present in the Play Custom Map screen.
It's all a bit rough, but should work, let me know if there's any issues!