Grumpy_Mike: You are going to generate the same amount of heat with any linear regulator method. If you want to reduce the heat then you have to use a switching regulator, there are a lot harder to make because you need a good layout on a PCB to keep the circuit stable.
And just to reiterate - using a current source for the LEDs, you do not need to feed them from a voltage regulator.
I think you are misunderstanding this statement.
So again, the LM317/7812s would go away.
No, you replace it with all those transistors that generate a constant current supply.
I would not endorse the advice given by cjdelphi
He asked for suggestions... now get off your soap box