Your gapped toroids are much more "proper" than mine! I just put the toroid in a bag and smacked it with pliers
LOL ... thats the Neanderthal's way of breaking ferrite core.
I guess that leaves lots of other unusable small pieces, and ended up with a ugly core with tons of chipped surface, just becareful on those rough surface, they may scratch the copper wire.
My method is to wrap the core with some soft cloth, the secure half of it in a vise, while using plier or even better using vise grip to clamp the other half, then blow the vise grip with a small hammer. That will ended up splitting the toroid core into two pieces without any chipped surface and nice & smooth join.
To glue it back in one piece seamlessly, I use PC-Fahrenheit epoxy, and capable of yielding a really tight gap. Sort of controllable gap creation, and the increase at the core saturation is like only few times rather than wildly hit & miss results that sometimes ended up with too low core permeability to be usable.
Interesting experiment, while running with this circuit, try heat up the core like blowing it with warm air from hair dryer, sometimes you can get interesting results when the core is heated up or cooled down.