Force between two electro magnets
The mistake is assuming the metal core will be saturating. This might be the case should the core form a complete toroid but it doesn't - the major influence on the flux density is the air - think of the ferrite core being in series with a longer air gap - magnetic flux has to travel through the core then thru a much longer length of air before returning to the core. The core may not be anywhere near saturation.

The formula for the attractive force between an electromagnet and a ferrous material is: -

Force = \$\dfrac{F_M^2\cdot \mu_0\cdot A}{2\cdot g^2}\$


where Fm is the ampere-turns of the coil,
\$\mu_0\$ is 4\$\pi\times 10^{-7}\$, 
A is area of cross section of solenoid and 
g is the gap to the piece of metal.


Maybe this formula will help - I'd imagine the force would be twice that given in the formula due to two coils interacting.



EDIT: -

If the mean length of the H field is about 2m for each coil, with 70 amps and 200 turns the H field is 14,000 ampere-turns per metre. To calculate B use the formula B = \$\mu_0\cdot\$ H. Because the field is 99%+ dictated by the air gap on each solenoid \$\mu_0\$ is largely valid. B, flux density then works out as 17.6 mT i.e. nowhere near saturation. Of course the mean length of the magnetic field could be much smaller than 2 metres but it's unlikely, given your quoted dimension of diameter to be much below 0.5 metres and this would make B 4 times bigger at 70mT but still not close to saturation.