I suggest simplification...this is what I've done in the past: Assuming the load will be more or less the same and not a lab variable power supply or one whose load changes significantly, drop the transformer secondary+rectifier+first capacitor voltage with power resistors until voltage is just 10 or so volts higher than the needed voltage. Then LM317 will drop another 3 volts giving a 7 volt margin to allow for summertime utility company voltage sag. Each of the power resistors can be and should be followed with another filter cap so ripple voltage at input of the LM317 is low, no more than 2v p-p, but should be easy to get it down to 1v p-p. These voltage dropping resistors might be in the range or 100 to 150 ohms (assuming 2 such resistors) and about 1 watt in which case I use a 3 watt resistor, for instance standard size metal oxide, not hi-performance small 3 watt cuz I want surface area for power dissipation. The resistor to GND on the LM317 adj terminal will be running around 1.8 watts so use a 3 watt there. In pic, the 620 ohm resistor is the hv dropping resistor and the 2 100kohm resistors in parallel are the adj terminal resistor....I needed 50kohm 3 watt but only had 100kohm on hand so that's why two of them. Becasuse there's not much volatege across the LM317 only a modest heat sink was needed. I used an LM317HV though that probably wasn't necessary but the additional cost was negligible so I went for it. Also, note I put two 6.3vac secondary windings in series, then regulated down to something like 8 volts, then dropped with chassis mount power resistors down to 6.3 vdc for filaments. The small transformer is for +48vdc phantom power. (Using an Antek transformer, forget the model num)