The two URLs aren't identical at all.
Correct, easiest way to test http/https was to create a new site collection
My knowledge of SP is limited. . . Is it possible to right click on a PDF and copy the full link to the PDF?
https://sys-testsp.acmecorp.com/DocTest/test.pdf
What's the dot version of SP?
SP Foundation 2010 SP2
Has any 11.x Acrobat product version ever worked for you over SSL?
First time we tested with non SSL/SSL.
Other PDF products do not have this issue with either setting.