Just a suggestion. Has Bitrix24 considered integration with Box (https://www.box.com) or Dropbox for file storage as an alternative to using the native storage system? Other project management software such as Teamwork also has this capability.
I'm just trialling Bitrix24 but am a fan of Box.com and would support Edward's suggestion. However, I've just tested your Dropbox integration and was disappointed to see that you don't actually leave the job of storing the file with Dropbox - so if I want to reference the same file twice in Bitrix, it will actually upload 2 instances of the same file!
I suggest your team look at how TeamworkPM integrate Box.com into their system - the file isn't actually uploaded into Teamwork, it remains within Box - which has to be the right approach.