I have been learning quasicategory theory in an attempt to understand higher topoi, and I have been trying to look at as many different sources as possible. Higher Topos Theory provides a higher categorical version of the Yoneda embedding, but it requires leaving the Joyal model structure on simplicial sets and as far as I understand requires a difficult path through many different model structures through the process of (un)straightening.

I know that Cisinski has recently published a book in which he develops the Yoneda embedding internal to the Joyal model structure. So here is my question: can chapter 6 of HTT be understood internally to the Joyal model structure using Cisinski's methods? Are there any difficulties other than the Yoneda embedding present in that portion of the theory that require leaving the Joyal model structure? Is it even worth it to learn in this way, or should I just bite the bullet and understand (un)straightening?