Your assumption is correct. As you approach saturation, B-H curve flattens out, meaning that a further increase of magnetic field strength does not result in an increase in flux density. So, the solenoid force will drop just as you predict for a given gap length.
Solenoids designers are generally concerned with starting force, because it takes less magnetic field strength to get the steel magnetized as the gap becomes smaller. As a result, solenoid drive circuits are often often designed to charge capacitors to provide high initial current to get the load moving, or start with a high current and use PWM to drop the current after closing.
An annealed low-carbon steel like 1018 will have a maximum flux density in the 1.5-1.8 Tesla range, and exotic cobalt alloy materials like VACOFLUX achieve 2.4 Tesla. You should design such that the starting (full gap) flux density in the flux path at the point of lowest cross sectional area is below these values. Otherwise, you will be supplying more current than necessary to magnetize the steel to its maximum.