You don't need to actually die. Just need to start the reaper raid and then let it end it somehow, whether by letting the raid target be captured (easiest), killing Death and his apostles, or just timing it out.
Once you started a Reaper Raid (with the Bell of Darkness crafted from the Chaos Workbench) and let it end, a green quest marker will appear at the SW part of the "chaos wasteland" map to the northwest. Going there will give you a cutscene with a Lost Soul giving you a fetch quest to
hunt twenty bear asses retrieve soul drops from the Reaper and his flunkies. Completing the quest restores the Lost Soul and lets you recruit her.
Overleveling is counterproductive for the Reaper raid. It's best to just draft your existing workforce for this, and the lower leveled they are, the better. Most of the grind is to get the mats to craft 100x Steak Set or Veggie Pizza. (Or to capture firebomb-lobbing units, if that's the approach you'd prefer.)
Chainsaw is ideal to defeat the Reaper (not counting macro'd multihit exploits with any random weapon), but other multihit weapons can work in its place. Easiest one to get your hands on is the shuriken, crafted from the Spring Workbench (trade with Trader for it).