Spock is making hurry a priority by his odd choices. Why strive to reach orbit immediately? That only makes Scotty work under unnecessary pressure, possibly leading to mistakes. Why drain the phasers so soon? This could be done at any point, just before the chosen time of departure. And firing at the natives would not drain the phasers, unless the cavemen arrived in the thousands - "Omega Glory" teaches us that much.
Staying put for a week should be an option here, and a fairly safe one at that. Outside rescuers would have great odds of success; the castaways had virtually none. Doing nothing (except burials and a perhaps a friendly game of baseball) would be a perfectly valid survival tactic, if not for Spock's oddly biased approach to the crisis.
Really, the sooner the Enterprise
left, the better. She would be back all the sooner, too. It would take three days to make the scheduled rendezvous. Or just two if Kirk called ahead after the first day of sailing, caught the Yorktown
at the rendezvous spot, and asked her skipper to come meet the Enterprise
one-third way in because of the overriding emergency. Kirk would be back in four days, then. If the additional two days for the delivery of the medicine were not possible, it would be the aforementioned six days, within which none of our castaways would yet have to go cannibal. And there are always higher warp factors...