The universe appears "old", but it is still less than 10,000 years old

[Alex K]

I think in the "geocentric" synchronization convention, Romer's measurement would simply be interpreted differently: the moon appears to be covered later by Jupiter, because they have increased their distance and have therefore gone to a distance where time is lagging behind somewhat. Remember that in this slanted "geometry", moving around in space radically changes your time frame. Romers interpretation of the delay in terms of travel time simply assumes that time on Jupiter is the same as his. This is also roughly what you get (up to time dilation due to movement of jupiter) when you use standard SRT synchronization convention. The anisotropic picture is an artificial mess, don't get me wrong.