The Panels module provides the panel element "New custom content" which is simply a node-like edit form. It allows to choose the Input Format too.
better_formats_form_alter() to allow Better Formats to step into the Input Format part of the form. It's a one liner so I just copy the changes here:
case 'node-form': case 'ctools-custom-content-type-edit-form':
I did test it with Panels 3.2.