Qwarp registration to the TT_N27+tlrc brain should be done by blurring both the base (TT_N27) and the source datasets. The auto_warp.py script doesn't allow for this, apparently. You might get better results with a modified 3dQwarp command, but that won't fit into the afni_proc.py schema at this point in time.
Rick is out for the next 2 weeks, and changes to afni_proc.py will have to wait until he returns. Sorry.
If you want to try a modified 3dQwarp command, you can use the 3dinfo command on the output to see the command that produced the "droopy" file, and then re-run 3dQwarp with some extra options, such as
-blur 3 3 -workhard:0:1
to see if this helps cure the problem.