This is getting tiring. We do not observe homogeneity in the radial direction
. We don't expect to, because the radial direction is also looking backwards in time.
What we observe instead is a universe that looks like the nearby universe is a later version of the far away universe. In other words, it's as if looking outward in space is looking through a succession of homogeneous equal-time slices. This is the standard cosmology. This is what we observe. None of our observations contradict this, and it is fully self-consistent.
As for the BAO paper, if you look at their data, the apparent [itex]3\sigma[/itex] deviation is represented in figure 6, where you can clearly see that the discrepancy comes down to the signal being rather noisier than their simulations estimate, which would be indicative of not properly taking something into account in the simulations.
A perhaps better paper for this particular issue is this one:
...because this shows the combination of WMAP, supernova, and BAO data. The relevant plot is fig. 13, where you see that the contours all converge on the same point in parameter space when these data are taken together.