Looking at satellite imagery, Cindy is definitely trying really hard to get organized. Outflow is improving in the right half of the storm, as evident from the cirrus banding features that are elongating over the past few hours. However, the west half is still choking. The deepest convection is trying to wrap around the west, but the shear will not lighten up enough for it to do so. Overall organization looks better now than this morning, but only very slow strengthening should occur. Wave observations from buoys do not indicate much above 12 feet, so sustained winds of 60 mph right now are a bit of a stretch...or only present in a very very tiny location.
If Cindy deepens a little bit more, it is all the more likely that it will follow the upper-level flow regime and shift east. Right now, it looks like it may clip the outer tip of southeast LA, then continue towards the MS coastline. Depending on how deep the system is, it may even clip the Florida panhandle - most likely after landfall.