With the tapered tuners that Lakland uses, you don't need that many winds. If you're used to playing Fenders that don't have tapered tuning pegs, Fenders require you to wrap several times. This provides the proper down force on the tuner to create the proper break angle over the nut. With the Laklands, you only need about 1 1/2 winds max. The tuner provides the proper down force across the nut.
By adding more wraps, you're not really gaining anything and are running the risk of creating a twist in the string. This would be my guess as to why they're breaking at the point that they are. If you hand wrap the string around the peg (before you start tuning it), there might be a slight twist in the string. Also, you might look for a burr on the tuning peg. It's unlikely on a new bass, but it is possible.
If you can't figure it out, drop Leo Lopez a line at Lakland. He's awesome and should be able to help get it straightened out.