I like when somebody tries to think of time as something other than the way we are accustomed to.
I ultimately think this is what is necessary to solve certain problems we face in Quantum Mechanics AND Relativity. (Getting away from the usual train of thought regarding time.)
In your analysis, (particularly the travel to the center of the universe idea,) I would have to ask how we determine just where that is. Current Cosmology considers the universe to be expanding from EVERYWHERE, and does not define a given point as the center. (See my ramblings on the "finger point" problem in another thread.) It has to do with the (assumed) fact that time AND space originated with the big bang, and there is thus no specific point that CAN be defined as it's center.
Frankly, I have a problem with this myself, but I've yet to ask a Cosmologist that can explain it in terms I can understand. It would seem that we SHOULD be able to define a point of origin shouldn't it. But...
The Astronomers and Cosmologists say no.
It is also DIRECTLY related to why I thus far say Time Travel is not possible since it is not possible to accurately define ANY point in space, relative to the universe as a whole. At least no one ever has.
So your stuck with the problem of just exactly where your "time machine" is going to deposit you. (Past or Future.) Since you can't define exactly "where" that place was/will be, that you intend to travel to. Even if you could solve the time issue itself which despite several claims to the contrary, we haven't.
If we ever do, (assuming that it's even ever possible TO do,) it won't involve the use of "Time Machines" or any specific ability to "travel" to "the past" or "the future". They don't really exist do they. We fool ourselves into thinking they do, but in reality, they are only figments of our imagination and nothing more. Besides, any such scenario ALWAYS sets up the possibility for a paradox. I don't believe there ARE any paradoxes in the universe, hence, no possibility of "Time Travel". Not in the aformentioned sense anyway.