It is not clear whether you need a platform to help you manage the project or the platform itself will be an integral part of the project. The list of specific tasks you list can be supported in Moodle one way or the other. You could use the central Moodle installation (and thus normal logins) if the administration is willing to set up a separate category for your project and assign you several course areas (project areas for you). You can also consider running your own Moodle instance, sounds you should be able to on technical level, and have more freedom to control and customize Moodle to your needs. You could possibly use the same authentication mechanism as the central Moodle, so users would have the same login to both.
Moodle has a number of standard and 3rd party module and blocks for you; for example:
Main Project Page - Section 0 of course area, html block, webpage resource
Planning/Ideas - wiki module, calendar block, tasklist module
Task assignment/schedule area - probably custom-made using database
Discussion Area - forum
Document Area - folder resource, one of the repository options