If you read the very first post in this thread you will find this statement.
* White Wyandottes and *White Plymouth Rocks are not a good choice. They sometimes have the correct genotype to produce sex linked chicks and at other times, they do not have the correct genotype to produce sex linked chicks.
The problem is that there are different ways to make white. This does not necessarily involve Silver which is needed to make red sex links. Solid white hens may or may not be OK to make sex links. From what you wrote, the hens do not have the right genetics. The New Hampshire rooster should work fine with the right hens.