Text Stroke Comes Out Messed Up When Exporting

I agree. The only way is to duplicate the textframe on top of itself. The duplicated textframe on the top would only have a black fill; not a white stroke.

I like the effect you have designed!

There is no solution, so to speak, but here is a possible workaround, as clunky at is:

What I would do if you want that size of stroke, is to have two layers. One where the type is WHITE with your big white stroke, then duplicate the text block on top of that where you make that type Black with NO stroke.

The other option is to use a Outer Glow effect instead of a stroke, like so:

Your stroke is too large, so it has started to overlap the type below.

When type is rendered it starts with the first character of the first line, just like as if you were typing it., so when it gets to the following line, the white stroke is covering up parts of the previous line. e.g. the line with the word "make" is covering up the line above it:

Adding to your problem, in a PDF, to maintain positioning, some lines of type will be broken up into separate objects, so the same thing can happen within the same line, like so, where there is now a break before "promise":

Does it show only on the screen? and if so, what are you viewing it with? Does it show when printed also?

Can you send a sample "wrong" PDF up for us to look at?