> So the trick is to do the computation forwards, but take care to only use reversible operations, store the result outside of the auxiliary "full" memory and then run the computation backwards, reversing all instructions and thus undoing their effect on the auxiliary space.

If the results were stored outside the auxiliary "full" memory, there wouldn't be any need to reverse storing the results. So you probably meant the opposite: store the result inside of the auxiliary "full" memory.