Yeah, urgency is big driving factor for a lot horror games but there are plenty that did well without it as well. You could try adding a timer or a reverse loading bar when selecting text options or just searching around in a room, if you wanted that moment of panic. Maybe you could try quick time events if you like.
For the text breaks, a good example I can think of is during the demo where the shaking "YOU ARE WORTHLESS" appears. The "less" is truncated and goes to the next line which breaks the immersion a bit. Perhaps if you play around with the spacing of powerful statements such as this you could have one word on each line centered or flowing diagonally. The majority of the text so far in this demo is solid. The shaking text really makes it feel more interactive. Characters have their own text color which is awesome and they provide a paragraph gap after they finish talking. (except for that one time where Chris slapped his belly) Staying consistent with text spacing will go a long way so when you break that consistency on purpose it sends a different message in a strong way. I hope this makes sense haha.
I would love to see your future builds and help you out in anyway I can. I don't mind either way to communicate via twitter or here in the comments. Good luck on your project!