Have you done the magic marker test? That seems to be helpful to see if you are getting to the edge along the length of the blade.
Depending on the condition of the edge, I would think it could take a lot more than the circles/strokes you're describing on a 4k. I've had ebay edges that take a lot more than that on a 1k. Just depends. Do you have any pictures? Maybe the experienced honers will chime in.

Shane