Maximising the strength of an electromagnet
If you look at the force generated by a solenoid you will not normally find a term in there for the permeability of the solenoid core: -

\$F = \dfrac{(N*I)^2 μ_0 A }{ (2 g^2)}\$


N is number of turns
I is amps
\$\mu_0\$ is permeability of free space
A is cross sectional area of solenoid
g is gap between metal wishing to be attracted and one end of the solenoid


This is because the flux produced to attract another piece of metal is mainly flowing through a large air gap. This air gap totally dominates and should not be confused with dimension g in the formula above - g above is the gap between one end of the solenoid and the metal to be attracted BUT flux then has to flow out of that metal and back to the other end of the solenoid (a much bigger gap).

However, should you have a solenoid that is attracting the metal with both pole pieces i.e. one constructed from a simple transformer core then this is improved. However, the path that the mag field takes is still thru a significant air gap and the magnetic reluctance of this air gap will still likely dominate the low reluctance of the core except for very small gaps.

Reluctance adds in series like resistors in a conventional circuit and clearly 1k in series with 1 ohm is still largely 1k.

If you are using a single ended solenoid (I have no idea what a MOT is) then abandon the MOT and make your own from much fatter gauge wire so you can push the current through it. Make the cross sectional area (A) as big as possible and stack the windings as close to each other as possible.