The decision to not use the main (CSM) engine to stop them and allow them to drop back to Earth was made early. Having already had an explosion–as well as possible damage to the engine bell itself–it was felt that it was too risky to relight it, hence the “free return” option.
Knowing what we know now, would that have been a viable (relatively safe compared to free return) option?
The problem is, we still have no way of knowing if the main engine was damaged or not. It might have held up through the turnaround burn, or it might have refused to fire, or it might have failed halfway through the burn and left them on a trajectory that they couldn’t return to earth with even with the lander engine. In retrospect, the decision to use the LEM as a lifeboat and to use the descent engine to get back on a free-return trajectory was still the safest one.
Knowing what we know now, is essentially the difference between the decisions made during the mission to the knowledge after - which was confirmation of explosion source and reasons for it, and the fleeting pictures of the side of the service vehicle. Those last pictures really confirm the decision not to use the main engine. With the entire side of the vehicle blown away, and a clear mess of damage. Seeing those pictures during the mission would have made the decision not to use the engine instant and not subject to much debate at all. Almost anything could have failed with vastly worse consequences than their existing predicament.
The use of the free return, and in particular the fact that they would take significantly longer to return actually worked in their favour. Although the crew were critically tight on power and water, mission control needed every last minute of the extra time to work out how to get the crippled craft back. A direct return was actually possible using the LEM, but it would have exhausted all the fuel and had anything gone wrong left few options. The creed of mission control was to never make a decision that cut down your options until you had no choice. Indeed they always made decision as late as possible for just this reason.
Although the discussion was highly dramatized in the Ron Howard film, I doubt there was ever a serious discussion about anything but a free return trajectory. The explosion and rupture of the oxygen tank occurred at nearly T+56h when the Odyssey was over 320,000 km from the Earth, already within the Moon’s sphere of influence or very nearly. In order to kill the speed of the CSM and turn around would have required far more energy than the free return trajectory, and even if the CSM main engine had been functional I don’t know that it would have had sufficient impulse to effect a faster return trajectory than a free return, which is actually just about as fast as the capsule can return and safely reenter the atmosphere. Using the LM descent engine to slightly modify the trajectory for a free return was the simplest, safest, and probably fastest way to return.
BTW, despite the presentation in the film of the concept of using the LM as a lifeboat as novel and improvised, Grumman had studied this contingency extensively, and while the plans were not part of NASA’s mission procedures or included in the handbook, they had been documented. Upon hearing of the problem with the Apollo XIII mission, literally thousands of Grumman engineers and technicians reported to Grumman or the NASA facilities at which they worked and immediately started working on the problem of using the LM propulsion system and life support to return the CSM to Earth. Grumman later proposed using the LM chassis and propulsion system for a number of “space truck” roles with both the Apollo and Gemini systems as well as for a number of proposed space stations.
Stranger