Have you tried using some of those icing tip covers over your tips in the bags you have put aside? I know Wilton makes them, and probably so do others. I think they are made of soft plastic or silicone.
I don't use metal tips for piping and flooding, so if a dry plug forms in the hole of my piping bag, I simply push it out until the icing flows again. Sometimes, I also have to knead the bag of icing to soften it up to the right consistency again. If kneading doesn't do the trick, I squeeze the icing back into a bowl and whip or whisk it up to consistency again, adding a few drops of water if needed.
Edited to add: As for piping/flooding "bonding" together seamlessly, try piping then flooding smaller areas so the piping doesn't have a chance to dry or begin to crust over before you flood into it.