How to choose Toroid core to improve DC current measurement
If you are going to have an airgap large enough for a Hall element, then it doesn't really matter what magnetic material your core is made from, the reluctance will be dominated by the airgap.

I would strongly recommend using two Hall sensors, one in each gap, in phase to circulating flux, outputs added. This will reject external fields, to the extent that the gaps and the sensors are balanced, as the Hall elements will be in anti-phase to external flux.

Your scale factor depends almost entirely on the size of the airgap. You have to control this precisely if you have any pretension to repeatability or measurement accuracy. To this end, you probably need to embed your sensors in something thin, stiff and flat, so that the clamped cores come together with a well-defined geometry. You can't simply have them rocking on the sensors themselves and expect mechanical stability. The something obviously has to be non-magnetic, but non-conductive would be good as well if you want to measure changing currents. Perhaps a strip of bare PCB with a pocket cut out for the Hall sensor, or cast araldite resin.