I sometimes use LaTeX to create a PDF file which I can view in
full-screen mode and step through it page by page but with no scrolling,
imitated page turning, sliding, and so on. The main reason I want to
page through instantaneously is so that I can build up a slide with
bullet points line by line. Every PDF viewer I've seen can do this,
except those for the iPad. I downloaded 6--8 from the App Store and
none of them seem able to do what I want.

The closest I've come is with the native Books app, which has the full
page and individual pages as icons at the bottom. Thankfully, I have
VERY thin fingers, so can get what I want by tapping them one by one.
But that is error-prone, especially when giving a presentation. What I
want is similar functionality just by tapping.

Any ideas?

(Of course, I don't actually write several pages, each with one bullet
point more than the previous one. I write a normal LaTeX file with just
the complete pages. I then have a script which reads it and creates
LaTeX files for the individual pages. Via nested \input commands in a
new LaTeX file to the desired structure is created, optionally including
a footer or whatever. (Thus, even in the script-generated files, there
is no text duplicated.) After the last page, the completed pages are
\input one by one so that I can easily "go back" to a given slide.
While I've often seen the line-by-line structure, which presumably many
packages implement in a similar manner, I'm surprised to see a speaker
stepping back through previous slides line by line. I started this 25
years ago. There might be presentation packages which do something
similar, but I am content to concentrate on the logical structure and
have it come out looking like I want it for a presentation.)