The best way to use a flux concentrated DC Hall is like this
Blue is ferrite or iron, black is the two Hall devices.
First, note there is no milling out of pockets with a Dremel for the sensor to sit inside. This way, there is a large consistent air-gap to lower the overall permeability of the ring, to prevent it saturating with small currents. You've not provided a picture of how your Hall sits in a groove, but I suspect it allows the two halves of the core to touch. This (1) allows most of the flux to bypass the Hall and (2) with no airgap the cores saturate at low currents.
Second, there are two Hall devices, one facing up, one facing down. The electronics adds the two signals together. This tends to reject any fields in the sensed gap caused by linear external fields, while doubling the sensitivity to fields round the core caused by the current. Alternatively, you can have the two Halls facing up, and take their difference, which might be easier to do in a bridge configuration.
The gain of this configuration is linearly sensitive to the length of the airgap, for high permeability magnetic material and small airgap. Take some precautions to make the gap consistent, for instance with a non-magnetic spacer like aluminium, if you dismantle the device between calibration and measurement.