Are you going to use Norne as the MVP for carrying yourself over Astra Season? Is she the main tank and / or relies on a mixed phase duelist?
Guard Bow with Distant Defense and Distant Guard are good enough and helps her survive some AoE specials.
If your plan is to counter Thrasir and units that rely more on speed and not so much on attack, then Devilish Bow is a great option to not allow them to charge their specials unless they’re pre-charged at 1 or 0 and have Flashing Blade.
I wouldn’t advise Slaying Bow or Short Bow because they don’t provide a defensive strategy and Norne really needs them.
As for your strategy and team synergy, it can work well on many teams, but I can picture some attempts where you might fail to kill everyone and lose on the next turn or when the countdown ends. And that’s where you have to ponder what’s more important: Staying healthy and restore the lost energy caused by Upheaval and Bolt Towers or reducing enemies’ defenses with Moonbow, Luna or Glimmer.