Ok I'm trying to help you solve the problem a little.
First the answer for couple of your question.
Q - Am I overlooking something?
A - No. There is a PHP PDF library that can replace placeholder variables in an existing PDF and generate a PDF file as the end result, without screwing up the layout
Q - Is there a way to do this using PDF forms?
A - Yes. absolutelly the tric to doing this is by using a PDF Forms
For both answer you can use Justin Koivisto fill pdf form field php library.
For more detail you please go to http://koivi.com/fill-pdf-form-fields/tutorial.php.
Take a look there for additional information.
Credit to Justin Koivisto for his work
P.S
For workaround for displaying a table like output from pdf form
please consider to take some reading on Oracle Business Intelligence Publisher User's Guide - Creating a PDF Template