demi-?
Actually, I’m going to disagree and say death is a process that cannot be tied down to a precise instant. So nyah!
Is the project dying but not dead?
Is it terminal or preterminal or moribund but not dead?
I wouldn’t hesitate to create a neologism if you want to mock the “mortem” part in particular. In that case, perimortem is what you are looking for. Make it peri-mortem or “peri-mortem” if you want to call attention to the fact you are aware it’s a neologism.
An interim somethingorother - evaluation, analysis, etc.?
Progress report?
The antepenultimatemortem report? 
The project so far…? (right behind ya, chappachula! )
As one who has presided over plenty of deaths, I agree.
Once one of my residents pronounced a patient prematurely. That will definitely ring home the point that it’s a process.
Instead of being annoyed at incompetence the family was delighted with their miracle. Go figure. Sorry for the hijack.
[The Dead Body That Claims It Isn’t]
I’m not dead.
[/TDBTCII]
Not a prefix, but in media res works. Literally. It’s a favorite literary device of mine, actually.
I would vote for "meso- " as the general prefix for “in the middle”, based on words such as “mesopotamia” (between the rivers) and meso-america (middle america). however, I agree with posters who don’t think it fits the term “mortem”, as the teacher seems to be wanting it in this case.