OK well 450 mA is a fairly big current, thats why the voltage of your regulator drops.
Thats the same sort of reason why your "12V" power supply has 17 V with no load on it.
It won't harm the solenoid to have 17 V on it. I'd just have the power supply without having
a second regulator. Having two regulators isn't doing much for you except wasting power.
Saying the transistor need 1 A base current is strange. Is that an upper limit or a minimum requirement ?
If you need 1 Amp base current to get 450 mA through the solenoid, the transistor is not doing much good.