If at first you don't succeed...Ask for help, then buy an off the shelf solution.

Finally got the bigger solenoid working,  just ended up having to pull all of the current limiting resistors.  By work I mean I made the nail actually move, not with much force or very far, more worryingly the power supply was making an ominous hum the whole time it was plugged in.  For the moment I'm done trying to build my own solution, it would take way too long and far too much wire to wrap 56 of the damn things (for the prototype).  Ordered 10 of these pesky things.  Many thanks to +Michael Seedman for talking to me about solenoids and sending me this and other photos.

(surprisingly made in the USA)