Firstly,i think the first figure can not implement the bandgap with power supply smaller than 4v. Because the left bias is cascoded with four diode between two power supply, it causes the circuit works well in small margin range of power supply.
1. the design steps are determing the two legs current bias with respect to the power dissipation;
2. make sure the pnp unit emitter area current density, so to sure the ratio with two legs of pnp and consider the layout matching; Then, the resistor is determined by the ptat current;
3. in corresponding with zero TCF, make sure the pnp and resistor value;
4. maybe , i think a op amp shoud be used for stability the same level;
5. the last is to design the start-up circuit;