How can there be real space contraction of the universe.[/font][/size]
The problem with that question is that it is a lot like the question, " If the world is round, how come the people on the underside don't fall off?" in that it is based on a presumption. The presumption of the quoted question deals with the nature of "down". The presumption of your question deals with the nature of time and space (and how its measured).
Now I'll explain what I mean.
Imagine that you have a point "a" located at a position with respect to the origin of a reference frame like this:

We have two axes, x and y. If you draw a line perpendicular to the x axis, it intersects with the x axis at xa which gives the distance of a from the origin in terms of x. a similar line drawn perpendicular to the y axis gives the distance of a from the origin in terms of y.
Okay. Now we superimpose a new reference frame on top the first with the same origin but tilted at 45 degrees. The axes are labeled x' and y' we draw lines perpendicular to the axes and intersecting with point "a" like we did before.

If we now rotate this whole image by 45 degree, we can more easily see how this new frame measures the position of with respect to the origin.

Note that if you were to draw a line between "a" and the origin, it would be the same length as it was in the first diagram, what has changed is the distance in terms from the axes.
To relate this to relativity we change the y and y' axes to t and t', the 45 degree tilt corresponds to the second frame of reference moving with a velocity with respect to the first, and the x axis is the distance as measured along the line of motion.
"a" and the origin represent events that occur at certain times. ta and t'a is the time difference between the event at the origin and the event marked a.
shown here are the measurement of "a" with respect to the axes according to both frames:


The time difference and the distance along the line of movement between the origin event and event a is different for the two frames. This corresponds to time dilation, length contraction, and the relativity of simultaneity). Again, the line joining the origin and "a" remains constant. This is known as the space-time interval. What changes between frames is the time and space components of the space-time interval.
These diagrams are for getting the general concept across and aren't proper space-time diagrams, so their utility is somewhat limited.
The point to all this is that any measurement you make is frame dependent and that measurement represents "reality" for that frame and that's
all the reality that there is.
So from a reference frame moving with "with respect to the local region of the universe" ( I'll will not say moving with respect to the whole universe, because that actually has no meaning), the local universe does "really' contract. And from a reference frame moving at a different velocity, it will "really" contract differently and there is no contradiction in this.
It just comes down to thinking about time and space differently, just like accepting a round Earth required people to think differently about what "down" meant.