The tricky thing here is how a linear regulator works, one way or another it turns the difference between Vin and Vout to heat. Pare the circuit down to just the 7812 and it doesn't matter what variant you use, it's still gonna dump all 3.3 watts (if I did the math right) of excess into the heatsink that may or may not be adequate. That is one trap with linear regulator ICs, you usually run into thermal problems before the current rating. Plus then you won't be sending the intended 11.3 volts, and they must be doing that for some reason, further research indicates this may be to induce more of the "tube sound" distortion.
I suppose you could replace the resistor with something like a larger case 3W one or 2 100Ω@2W in parallel to help keep it from cooking the PCB, but the biggest liability I see is that little 47uF cap (which keeps the 7812 from oscillating) getting cooked, use a long life 105*C part. Another thing you can do with hot running axial diodes and resistors is space them off the board something like 3-4mm.