You could always explain that reapers aren't necessarily bound to only one universe - heck, in Discworld there was actually a Death of Universes ;-).
Jack could have been an appointed reaper to the universes in which both humans and sentient furs exists (or used to be in the past). A rabbit as reaper would never be believed in at human-only universes. A new reaper can be introduced with the excuse that Jack had too many universes to pay attention to.
Your latest idea works too. Nemi, Reevo and Kerr could be originally from Jack's universe and Jack had to cross-over into PSI's world to collect their souls.
My 2 cents for today
Jack could have been an appointed reaper to the universes in which both humans and sentient furs exists (or used to be in the past). A rabbit as reaper would never be believed in at human-only universes. A new reaper can be introduced with the excuse that Jack had too many universes to pay attention to.
Your latest idea works too. Nemi, Reevo and Kerr could be originally from Jack's universe and Jack had to cross-over into PSI's world to collect their souls.
My 2 cents for today