Pulling the bullets first might be a lot safer. But with that much work, I don't know.
I think I would just keep them separate. In 223 556 that is not unheard of. I can load to longer COAL in one rifle, and do. But those rounds will not chamber in another rifle with a tighter chamber. You need two guns anyway: one for each hand.
SHTF is not a concern where I live. Which is not Las Vegas.