the magic of the market will select the most efficient alternative. At some point this may be no kids

Or, more precisely, less kids. I don't insist that we're guaranteed to switch to a lower birth rate as a species, but if we do, that's hardly an outcome to be feared.

Phosphorus will be a problem before oxygen.

Fascinating. That sounds right; do you know where in the Solar System we could try to 'mine' it?

The volume we can colonize in a given time goes up as (ct)^3.

Not until we start getting close to relativistic speeds. I could care less about the time-dilation, but for the next few centuries, our maximum cruising speed will increase with each new generation. If we can travel at 0.01 c, our kids will travel at 0.03 c, and so on for a while. Since our cruising velocity V is increasing with t, the effective volume we colonize per generation increases at more than (ct)^3. We should also expect to sustainably extract more resources per unit volume as time goes on, due to increasing technology. Finally, the required resources per person are not constant; they decrease as population increases because of economies of scale, economies of scope, and progress along engineering learning curves. All these factors mean that it is far too early to confidently predict that our rate of resource requirements will increase faster than our ability to obtain resources, even given the somewhat unlikely assumption that exponential population growth will continue indefinitely. By the time we really start bumping up against the kind of physical laws that could cause Malthusian doom, we will most likely either (a) have discovered new physical laws, or (b) have changed so much as to be essentially non-human, such that any progress human philosophers make today toward coping with the Malthusian problem will seem strange and inapposite.