earth - Sun as our Supergiant

When the Sun becomes a red supergiant (more accurately, an asymptotic giant branch star), it will have less mass than it does now. That is because mass is lost by an increasingly massive stellar wind as the Sun approaches the end of its life. As a result, the orbital radii of the planets would increase. The surface temperature of this future AGB Sun would be lower than the temperature of the Sun, but its luminosity would be much larger.

However, even if the Earth manged to avoid being engulfed in the outer envelope of the evolved Sun (which is still uncertain), the amount of energy received per square metre at the Earth's surface would be vastly increased over the 1.4 kW per square metre it receives from the Sun now. So your conclusion that life (as we know it) would be fried is quite correct.

The Goldilocks zone for the possible occurrence of life, uses the criterion of liquid water as the basis for allowing life to evolve. As a star becomes more luminous (and an AGB Sun would probably be about 100 times as luminous as the present Sun), the Goldilocks zone moves outwards roughly proportional to $sqrt{L}$, so about a factor of 10 further away.

The problem then with allowing life to evolve on another planet (e.g. Mars after its orbit has expanded a bit, or Jupiter) is that (i) you need the ingredients to be there already, or some way for them to be delivered, but more importantly (ii) there is little time for life to evolve, because the Goldilocks zone position evolves really rapidly towards the end of the Sun's life as the AGB Sun's luminosity increases - the timescales would be measured in millions rather than billions of years. Furthermore, the luminosity of AGB stars can be highly variable as they undergo big pulsations, which may also be a problem. (iii) After the (comparatively brief) AGB phase has ended, you would end up with a very hot ($T simeq 10^{5}$ K) white dwarf remnant that might effectively sterilise the whole system with ultraviolet light.

I don't think we know enough about how life gets started to say that these problems rule out your scenario; but they perhaps make it less likely.