I'm not sure what to put in here. I've studied this timeframe a lot, especially since I was a child living on a military base when the Cuban Missile Crisis occurred.
As a SAC officer, we studied the Crisis- a lot, and considered how it might be done if something like it happened again.
It was a critical time, since the Minuteman I was JUST going on Operational status, and the Titans and Atlas were just not as reliable as some of the historical records would seem to indicate.
There is the story the official records and the history book tells us...and the stories I heard from launch Officers who were there. But you're right. It was "Launch or lose" - particularly in the liquid fueled rockets. Once you started the fueling process, defueling and recertifying for flight was a several week process.
Retargeting the ICBMs was also a several day process, from what I was told. Over time it got faster, and now it can be done in minutes...but not in 1962.
Retargeting and recall was only slightly better in the bomber force, where there was a lot of fear that false messages would cause aircraft to uncover their targets.
The problem of returning with bombs from previously destroyed targets was covered by multiple target sets in the bombers.
Killing the entire NCA in Washington in one shot is either ASB or a severe violation of policy - depending on who you talk to, LBJ was already at either the Greenbriar or Weather Mountain during the Crisis, and communicating via speaker phone., not at the White House, as commonly reported.
But, in any event CINCSAC "owns the birds" if the NCA goes down, anyway.