Reported upstream at https://secure.phabricator.com/T6776 (merged as duplicate of Convert builtin fields in Maniphest to CustomField)
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This request should be proposed directly upstream, although something tells me that they are going to prefer the actual design, unless you have a strong justification.
Situation: T647. Old title "Ignore CC changes".
This Task was in project 'phawikibugs', indicating the context is 'phawikibugs', so I did not put 'phawikibugs' in the title -- just like we don't do that on bugzilla typically. However, this is confusing, as the project is only listed quite a bit lower on the page (as evidenced by comment T647#11134).
Conclusion: if even someone who has experience with Phabricator gets confused, chances are less-experienced volunteers also get confused.
Compare this to Bugzilla, where the project is the third element:
Another option would be to re-arrange the detail list, having Projects first instead of second last.
Looking at tracking tasks with dozens of blocking tasks (i.e. T2001), it might make sense to propose that projects are located between Author and Blocks. I guess the patch for this change would be simple.
I would not go down the route of touching the header, which is less convincing and requires more UI work.
I think just moving Project up in the list would already help significantly:
Which is also a well-defined request to upstream.
The solution lies in solving https://secure.phabricator.com/T5011 , after which fields can be re-ordered at-will.
This happened in the April 2016 UI update by moving the project tags into the box on the right, right under the available actions.
Hence closing as resolved.