Replacing the core of a solenoid to increase the pulling force
That probably won't help. The solenoid pulls on the wide part pulling it into the coil, if you start with the wide part in the coil it  will not be able to pull on any more metal in because it's already full. 

you best move is to get solenoids that are designed for the voltage you have available.

It may be possible to re-wind the soledoids you have, to make them work at a lower voltage. if there is a non-desctuctive way to disassemble them, if you take the magnet wire out and then wind it back on as two parallel strands you'll get a solenoid that works at half the original voltage.