Since I’m drawing a lot of inspiration from games like Space Siege, here’s how I’ve defined my player experience:
Player feels like a heroic, powerful, and futuristic sci-fi warrior, but also like enemies have harassed them just to the point of being overwhelmed.
I like the idea of keeping pressure on during combat sequences, since that will build a sense of relief when the player gets to a safe area, like a save room or a quest hub. The trick to this will be keeping the balance. I don’t want the stress to go on too long (I’m not building Dark Souls 
), but I want a sense of challenge and accomplishment in, hopefully, every encounter.
I’ve updated my GDD with the core player experience.