By all means leave the chapter titles. I think they will make up a big part of the charm.
I think in the case of a book like this it might even be fun if you added your own editor's comments on the chapter titles (as subtitles, for instance). Like "Mrs. Lovett Visits Sweeney (But Not in This Chapter)" or "Toby Falls Out of the Boat (And Mrs. Lovett Visits Sweeney At Last)". perhaps silly, but I'd enjoy it.
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