A minor niggly...
When talking about the interval between two events in spacetime,
WikTionary.ORG defines the word “ SpaceLike ” as:

“ [ two events ] lying outside each other's light cone,
so that no information can pass from one to the other. ”.

You wrote:
“ You may introduce more dimensions if you like,
but what do you want with an 'energy-like' dimension ?

I think about storing the energy into the rotations,
so its enough to stay with four dimensions.

The reason to think about this,
is the possibility to describe spacetime by quaternions.
Those have the intrinsic property of spin. ”.

Imagine 5 GPS-like birds shining well-regulated atom lasers at you.

With 4, you know X, Y, Z and T but ( I imagine )
the fifth would tell you the strength of your gravitational field,
thus improving the accuracy.