Another alternative (if you are not afraid to use LaTeX) would be Overleaf. While a learning curve exists you can layout documents beautifully with it.
I come from an engineering background where special characters and formulas are needed on a regular basis. We used Overleaf within our team to work on several parts of our document simultaneously.
Not for simultaneous work on one document, but maybe of interest for you: should you get off the grid for some reason, you can use offline editors like TeXstudio to continue working on your files. Once you get back online, you would still have to carefully merge stuff together, but there won't be many bad surprises in regards to formatting.
EDIT: I missed some of your points, sorry.
You can see where your colleague is working (there is a visible cursor) and who is logged in atm. I do not recall any other highlighting, though.
You can leave comments within the text visible for everyone working on the document - this might offer you the task management functionality without overburdening you with yet another tool.
As for deadlines... I did not notice any tracking functionality in Overleaf. I would personally use Gantt charts to organize myself, including milestones and the like. GanttProject offers everything I need, only used it offline though. But if you put the project files into some secure cloud storage or inside a git repository, it may suit your needs.
EDIT2: As Eric Lino pointed out in the comments, there can only be two people working on the document if you are using the free version (source: pricing list).