I tried mightily to have him say ‘I will finish what he started’, but no rendition of ‘he’ I could find worked at all. But perhaps it’s not terrible to leave it as is.

Placing the scene here as a prayer to Snoke definitely gives it a different energy, which to me is more of a ‘fanatical minion’ than anything else. I think it works for Kylo’s role at the beginning of the movie, and allows for different interpretations later. For example, right now ‘I will finish what you started’ could actually be directed at either Snoke or Vader. The Vader meaning has been well discussed, but if he’s talking about Snoke, it could be evidence that even now he’s intending to overthrow him and rule the Empire he built.