When current flows through a wire, the magnetic field spins around the axis of the wire. Winding turns ON the wire that is carrying the large current does not cut any of the magnetic lines. It lays in parallel to the magnetic lines. Putting a magnetic loop around the wire will allow the magnetic lines to induce magnetic flux in the core, and THEN you can wind a coil on the core, parallel with the current conductor, and it will use the magnetism to create a voltage. Without a magnetic core, you have to lay your pickup coil along the length of the wire to pick up any energy.What do you mean about 90 degree directional shifts? Thanks.
With a toroid, the magnetic lines go into the core and induce magnetism which you can pick up with a similar coil wound around the core.
You can either use a magnetic conductor to deal with the 90 degree angles or place (my) winding differently. What you tried is to get the magnetic lines to come out of the toroid through the hole, and they are much more interested in the magnetic permeability of the core.