How can I sacrifice a bit of DC Voltage to transform it to DC current?
You have a basic misconception, throw away the doubler and simply use a full-bridge rectifier. 

12Vrms is ~33Vpp. An ideal voltage doubler with no losses or load would turn this into ~66Vdc. 

All you need is to rectify the 33Vpp and you would get what you want. Assuming that the transformer and the rest of the elements can sustain your 1A, of course. 

But that’s essentially what you have actually built, albeit less efficiently. The reason you are getting 48Vdc is because the low load in the transformer is providing more than 12Vrms.