Hi Spiro,
Are you actually using little "transistor radio" 9V batteries? With 2 in parallel, 200mA is a very heavy load on them. You need 6 "D" cells in series to supply 2A.
I think that the 2A of limited current is killing the voltage from the batteries. Try adding a huge (10,000uF) capacitor across them to supply starting current.
If the motor is rated for running on 6.0V, its resistance is 2.5 ohms for it to draw 2.4A when stalled. When the current-limiter operates at about 2A, the voltage across the motor should be about 5.0V.
The current-limiter is not a switch, but is a linear circuit that continuously adjusts itself to keep the load current constant. Its output voltage will be zero only if the load is a dead short, or if the battery voltage sags 'way down.