10K Gauss = 1.0 Tesla.
This is roughly equivalent to an "airgap" line in terms of magnetic saturation.
At the OP's higher magnetic field (13k Gauss = 1.3 T), chances are the material is at least starting to saturate.
High likelihood that additional ampere-turns will be non-linear (i.e. need more than 30% change in amp-turns to effect 30% increase in magnetic field).