Capricious,
1) A pull out and put in replacement for the TL081 (change all 3) is either the MC34071AP or the TLE2141CP. Both are rated for 44V max.
2) Your project has heat problems:
a) The 2N3055 can dissipate 115W if you can somehow keep its case at no more than 25 degrees C. Its junction temp will be 200 degrees C. But it cannot conduct all its heat to your heatsink, because the surfaces are not perfectly flat (heatsink compound grease helps) and you have an insulator between them. The heatsink itself gets hot because it does not conduct nor radiate heat perfectly. A graph on the 2N3055's data sheet shows how much power must be derated from 115W in order to keep the junction temp at 200 degrees C, with increasing case temp.
Since your heatsink is 120 degrees C, the 2N3055's case temp must be much more. Assuming that the case temp is 140 degrees C, the transistor should be derated to dissipate only about 35W. If you set the output voltage to 4.0V and have a 4.3A load, then the 2N3055 has about 24.6V across it and 4.3A through it, which is a dissipation of 106W. Since it is dissipating 71W too much, its junction temp is probably about 308 degrees C. So you need a larger heatsink and/or forced air cooling with a fan.
b) The 2N2219 can dissipate 3W if you can somehow keep its case at no more than 25 degrees C. A heatsink won't help much because of its shape. If you set the output voltage to 4.0V and have a 4.3A load, then the 2N2219 has about 23.6V across it. If the 2N3055 has a gain of only 20, then the 2N2219 conducts 215mA. Therefore the power dissipation of the 2N2219 is 5.1W. Its junction temp is probably 323 degrees C.
I recommend replacing the 2N2219 with a TIP31A that is bolted to your project's metal case with an insulator and heatsink compound grease. It will not get hot. Also change R15 to 100 ohms for a reduction of its voltage loss.
c) The rectifier diodes are also much too hot. Replace them with a 6 or 10A bridge rectifier module that is bolted to your project's metal case.