Update - The "version 1" adapter ends up with pins labelled incorrectly (the 2 sides are swapped). Looks like it's because the 2 rows of the 1.27mm header are in the wrong location on the adapter board. A minor inconvenience, but if you use the version 2 adapter the pin numbering lines up ...

Not sure if you found a solution, but I had the same problem and was able to find a product that adapts to a 2.54mm male header and breadboard pin spacing. See links below. While these are not made specifically for the NEO4, they definitely have some potential. The kits include pin male pin headers ...