I am familiar with wfrp and agree it is punishing. It is a major factor in why I love it.
It is certainly hard to run it if you are worried about the combat. Are you worried about how members of the group will deal with said punishment? Are you concerned about how injuries may sideline the story? I don’t think either of these are the root problem you are facing, but if they are contributing factors it would seem like changing rulesets is advisable for this group.
I would love to run Enemy Within someday… for the right group. No sense slogging through it with a group that isn’t enjoying it and make it less fun for yourself as well.
In previous sessions I've let the characters push combats, starting fights when they weren't necessary or pursuing enemies who were already retreating in hopes of getting loot. They are newer players to RPGs in general, with most of their experience being in 5e, so I understand the disconnect between the system's expectations and what they want to do. Even though at Session Zero I tried to explain this to them, I think they had to see it in action.
The guy who pressed the fight for the loot was debilitated for the duration of his time in the campaign, which ended a few sessions later when he got a headshot from a crossbow bolt.
I've tried to be reassuring that even if they "only gather information" in a session, that is progress when you're running an urban investigation adventure. But they are bored, they want to pick fights, they are overwhelmed with the number of people involved and how to deal with the authorities or nobles.
I just think we're going to keep having a bad time, knowing what the adventure has in store. It's not like it's going to turn into an action-packed adventure - the system can't handle it.
As far as "sidelining the story" is concerned, as I've tried to tell them, the story will happen. If the party can't stop it, it will happen. The party can go do whatever they want, but time marches on. And the focus can be on what the characters do.