Hi Kyle.
I have built a printable version of a report before. All I did was create a new report, did not add it to any collections and in turn only accessed it from the carrot next to the home button:

You can also add visibility rules to it so only you can see the report and in turn your users will not be able to access it and get confused as to why a duplicate report exists.
To create the report I just copied over all the elements from the parent report and tweaked them to be printable.Therefore you can keep all your filters/slicers etc.
Let me know if you want more detail or have any clarifying questions.