So... Soul Saviour mode, a few question

Just started the DLC today. I managed to finish the bloom difficulty with Pyro/Banished team, and then the Tangled difficulty with Umbra/Stygian, but i can't seem to beat the overgrowth at all, presumably because i need more than 2 souls to be available.

So a general question on the souls things. I see random ones are just levelling as I play and then i get them as optional wins after certain boss conditions. Do these optional wins count as unlocks of the next level for that soul? If i have Grump and see Grump II as a reward from a boss battle, is my soul permanently upgraded to II or do I just have a II for that specific run?

And for some of these other runs, even on bloom it seems like some factions are borderline impossible to get to the lifemother let alone win, the Lazarus Experiment lot for isntance, even doing the usualy "dogpile unstable onto the hero as a bomb" approach doesn't really have any effect anymore. Can anyone give me soem general pointers on the gameplay strategy in soul saviour mode? Is it more focusing on buffs/debuffs/DOT over raw numbers compared to the base game or what? Thanks.