I simply presumed that several hours had passed before they made the final jump. After all, there had been enough time to offer Lorca a medal and for him to suggest giving it to the doctor. I thought that time had just passed in the interim. It's not like the show runs in real time.
But, I love how they are tying up loose ends. Why didn't Klingons have cloaking at the beginning of TOS? Well, they did, but, Star Fleet figured out how to break the cloaking and it isn't until the Romulans get involved with their superior cloak that cloaking becomes a thing again.
Why aren't they using the spore drive? Well, either you enslave and murder a sentient species like the Tardigrade, or it kills your pilot/drives him insane/possibly does all sorts of bad things. Oh, and if that doctor dies, pretty much everyone who actually knows how to make and maintain a spore drive is dead. But, you can pretty easily see it coming why spore drives are a bad idea.
And I love how they expanded Lorca's character. He is a Star Fleet Captain in the old tradition, but, the war and his pretty deep psychological issues make him look like he is just a war monster. The back and forth about using the Spore Drive to explore was fantastic.
I look forward to a second half of the season looking a lot like traditional Trek with lots of exploration and whatnot as they try to get home.
On a side note, I do think it's very interesting that they've now made going home for pretty much every main character a very bad thing. Lorca will be courtmartialed and certainly removed of command, Michael goes back to jail, the doctor, if he survives, becomes a lab rat, his husband will lose his position because of the genetic manipulation that the doctor did. About the only character that actually has a reason to go home is Saru.