The - 1.2 volts is only applied to the voltage potentiometer, the 723 will maintain its stability, this montage has been proven effective, if not the other schematic is good too, i dont know many projects who need less than 1.2 volts ?? and for the - 1.2 volts you can use Ldo regulators too, better stability.
If you tweak the pin 5 and 6 on the 723 you may get lower than 1.2volts, i could go down to almost 1 volts.
Normally there is no other way to counter act the minimal output voltage unless you do something like this. If not you can build an power supply with op amps
like some mastech psus who goes down to a real zero volts, the circuitry is not very complicated to replicate.
You can have or build this circuit Velleman k7200 psu, its a very well build circuit, 1x 723 as the voltage regulator and 1x 723 for the current regulator.
https://www.velleman.eu/downloads/0/manual_k7200.pdfHaving a relais on a tapped transformer will help to minimize the disspipated temperature if you set low voltages.
your 2) assumption is wrong in part, the -1.2 volt will be substracted in the potentiometer voltage (and 723 feedback circuit) if set at the minimum, you will get to zero volts, and it will be -1.2v less than any voltage set for sure.
The important thing is never to get past 40vdc for the 723 supply pin, 25vac is going near that 40vdc (Full bridge rectifier) if you want to get past the 35-37volts output, you have to use an floating lm723 design. There is some 723 circuits on google who goes at 70vdc.
You have the rare 3 legged pin tl783 who does 1.2 to 125 vdc at the output, i managed to get a few of them, and build some psu, but the dissipated heat is enormous.
Thats why for now i use already build Ebay snatched psu's like Sorensen, Kepco Ate 75-8, an my newest Kikusui Pad70-5, they use ac phase scr controlled bridge rectifiers, they will dissipate only the required heat (power) no more.
Still my old 723 based psu is rock solid, but if i compare them for the same voltage and current settings, the 723 based one dissipate a lot more heat, i have active variable speed cooling on it snatched from an atx psu, and all my 2n3773 are matched in the HFe (gain) to have equilibrium in their dissipation on the heatsink.