Three weeks is excessive, in my opinion. The ones I started a few weeks ago were only a week drying and they are doing just fine. It's worth a try, especially if your alternative is to throw them out. We've still got a couple of hot months here in Florida!

one week is enough for cut to heal/dry up. Plumie cuttings take 60-90 to develop full rootball, so I think you have time. If you get any sort of cold spell, however, since your plants would be very new, they will require protection for sure. Young plants, if not looked after, will freeze/rot without protection. But the odds are very much in your favor for successful rooting.