Where to purchase the iron core for an electromagnet?
The 1018 core is working just fine, doubling the field is exactly what's expected.
The problem is the remaining air-gap in the magnetic circuit. Using the steel core inside the solenoid has more or less halved the length of air in the circuit.
To raise the B field further with the same H field (H measured in A/m, not T) you have to replace more of the air with iron.
In the case of a transformer, the iron core forms a complete loop, with no airgap. In the case of a lifting magnet, the iron forms an E, and the scrap metal that it's lifting sticks to the open face and closes the magnetic circuit.
Once you have a core and a return path with no airgaps, your 1018 will return the figures you see in the B-H curve.