Hi Xeviat!
My advice is - forget about the CR calculations. Forget about "6-8 encounters a day".
Just run the adventure as written. Sometimes, but not always, you make an encounter a real challenge, by throwing in many more monsters, or adding a few seriously tough ones.
Getting good at this is not a science the CRs can tell you. It's an art, a skill.
There's really only a single way to get good at knowing what the party can handle, and that is by practice! So stop worrying about TPKs, and just throw in some monsters there!
The party can probably handle it (once they're fifth level or higher). And if they don't, well, chances are somebody will escape with her life.
Talk to your players. Ask them if your concerns are their concerns. You might be surprised - they might be terrified at the "easy" monsters you throw at them. Or they want the extra challenge, and then they're okay with you learning as you go, they're okay with the risk of some rare encounter becoming "too tough".
That's okay. Bottom line: forget everything the challenge guidelines try to tell you, and don't listen to the replies that suggest you're the one doing something wrong. Fifth edition is very conservatively designed; good players will wreck its guidelines.
But YOU know there's always more dragons to throw at the party, so don't worry, be happy. Even if it gets a PC killed on occasion!