I'm not immediately aware of a way to cause a kit/pack to "despawn" such that it'll reappear where it should be. Simulating it manually shouldn't be too much trouble though.
1. Instead of using RemoveEdict simply use the inputs Disable/Enable/Toggle
2. Start a timer for 10 seconds (I think that's how long it takes)
3. Disable/Enable/Toggle again
4. Play the item spawn sound (look at the engineer dropping ammopack plugin for this)