Personally, I would change the demon from being a Plague Bearer to something else (functionally identical, of course). The trouble is that Plague Bearers always cause Nurgle's Rot and Nurgle's Rot is Always fatal.
I would be fine with the mechanics of Nurgle's Rot how it is written in the EiF book if only there was a cure. Either a rare item or hiring a particular healer or Dramatis Personae that can cure it and then leaves.
You could even make it that if the wound is washed out with holy water (i.e. consume one holy water per warrior) at the end of battle, there will be no infection. If you can do that after trade it would be a little softer, but you could make it a bit harder by making it so that it had to be washed out immediately after the game and before trade.
But because it can be cured it must be something other than Nurgle's Rot so the Demons must be something other than PlagueBearers. Filthwalkers, Pus Demons, Infectinators, etc. PlagueSmearers, Scourgegivers, etc. The disease could be Nurgle's Blight, Nurgle's Mould, Red Death, Pussy Flux (meaning involving pus - not cats.), Weeping Blotch, etc.
Using different demons would give you an excuse to model your own demons too.