However, the issue with this is that it doesn't feel natural for me. I have to think of situations and triggers that start the next block of story, which sometimes feels unrealistic or rushed.
This is always the most difficult part in story writing.
Knowing from where the story come and to where it goes, tell you what the next scene/paragraph/chapter should be, but not how it is effectively linked with the previous one.
When you look at books, they either switch when changing chapter, or by using a temporal ellipse (generally a "*" triangle between two paragraphs). The reader usually use those moment to make a break, or stop reading for today, what help to fake the transition. But this can't works for games, even when they are Visual Novels.
When you look at movies, they use a cutting plan (is it the English expression for this ?). The most used one is probably when the camera leave the action to focus on something, then it, more or less slowly, transition to something else, before returning what became the next action.
This is already more adapted to games. But still it don't really works as it, because actions are proportionally longer in movies than in games. It would lead your game to rely too much on transition, what isn't a good thing.
This having been said, personally I solved this problem by changing my point of view. Instead of searching how to start the next scene, I focus on finishing correctly the current one. It's easier to do, because you're already into the action. And, since it's the continuation, or ending, of something that is already started, it give you the starting point for the next scene.
By example, a really basic one:
The MC is in the living-room, he finished to talk with his sister. The next scene is supposed to happen in the kitchen and involve the mother. Instead of simply let the MC leave the room, you can use something like:
MC "Do you still have things to say ? It's a hot day today, I would gladly just seat and do nothing at all, not even talk."
Sister "Of course it's hot today. Why do you think that I only wear my smallest underwear ? To seduce you perhaps ? By the way, I Hope you remember to drink regularly."
MC "Well..."
Sister "What ? It's important to stay correctly hydrated with such weather. Go drink something."
MC "Yeah, I'll do it."
Sister "Now !"
MC "Ok, I'll go."
And it's done, you've your transition. The MC have a reason to go in the kitchen, and once he'll be here, you can start the next scene more naturally:
MC is taking some juice in the fridge.
Mother "Good, you need to drink a lot during hot days."
MC "Yeah, I know, sis already scold me about this."
Mother "And she's right..."
All you need next, is to slowly shift the discussion to the topic you want to address.
The same also works without the effective help of an external character:
Sister "and then, she was all, 'what ? you didn't liked this movie ?'. And I said..."
MC "Oh fuck ! Talking about movies, I still have the DVD I borrowed to my best friend."
MC "Well, I'll take it back now, before I forget again. Later Sis."
Then you can continue with MC being in front of his friend house. We know why he goes there, so we assume that before this he goes in his room to take the DVD.
Once again, you've the start of the dialog, and just need to make it shift to the effective topic of this scene.