sound you are not trying any sugestions by others, provide the follwing details 1st
1) how much is the resistance you measure between terminals?
2) what is the dificulty for you to change the size of the wire?
3) have you understood the idea how the calculations must be?
i know your problem is very simple but you are still strugling, say a nominal size of solenoid can stand a loss of 5W that can be discipated to atmosphear keeping a small temperature raise.
just checked you pictures, the idea of your plunger is wrong, you have kept the same airgap through out, so you cannot expect any usefull force from it, it will just adjust to keep its position on its centre. that may be the dificulty you faced when used low voltages.just look some standard solenoids how they are made, normally plunger will be the same length of the solenoid, but some portion is brought out with spring load so when energized it will completely go inside and it decides its stroke.
if you need a push one you have to have a extended small rod like a needle of (2mm dia) comming from teh same size of plunger as discribed above. see the picture attched