Of course, it's possible to build the whole process within 200 hrs. but actually tight.
So, your requirement includes 7 frontend pages/backend.
Usually, 1 front page can be done within 1 or 2 days.
Of course, this includes the backend code.
In this case, my main concern is UI/UX.
Cause, you know every user only see your frontend pages.
So, according to your design, that site's performance decides.
I'm a senior full-stack developer and have all the stacks you are requiring.
I'm fully available right now and can start it immediately.
Best Regards.