You have a furler... changing headsails on a furler is basically a bare-headed operation (unlike a racing foil where you can hoist one before dropping the other).
Unlike hanked-on sails, a luff tape sail is difficult to contain on deck, esp shorthanded, and esp in deteriorating conditions. A better plan would be to make the best guess for which sail you'll need and set that one up before you head out.
I think you'd be best to get a versatile inventory.. chances are if you really need a storm sail you likely wouldn't be heading out that day, esp at this early stage.
However if you choose to do so it sounds like your sailmaker's plan ( using a temporary synthetic stay) is worth a try.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)