i don’t think i need your shop to be closed actually as I think i know where your problem is.

as you are caching pages, the text we are talking about gets insert dynamically via js above the first element with class “wppizza-article”.

for reasons only you will know you have added ALL items additionally into a hidden div. as your first element with class “wppizza-article” is in there, i suspect the text you are “missing” is added there.
as the whole div/form is hidden that text is hidden too

the items you have in that hidden div, are also missing certain id’s in the class names which will stop some other things from working btw (though that in itself has nothing to do with the issue at hand, you’ll just have problems elsewhere at some point)

PS: entirely up to you, but i somewhat question the wisdom of having all items everywhere but hidden .
not only will it effect your load times, but also will you end up with elements with the same id and I would think searchengines won’t be too happy either if 70%+ of your page is actually hidden from the user (though that’s just a semi-educated guess)

sorry, but i really cannot help you there.
i know nothing about your pizza butler.

the only idea – of the top off my head – for you would be to add a dummy element with class=”wppizza-article” somewhere before your butler so the text would get inserted there
(maybe you can re-position that element with css to make it then appear elsewhere)

in theory (though not tested with your scenario) perhaps a simple

<?php 
echo do_shortcode('[wppizza category="!all"]') 
?>

might do the job ?

again – just an idea.