I "borrowed" KMSigma's PowerShell script, which exports the device templates, and converted it to export the reports.
I take absolutely 0% of the credit, as KMSigma had previously done all of the work.
I simply had to swap out the query, and that's about it.
Using PowerShell, you should be able to export all of your reports, in separate XML files, to the directory of your choosing.
The only real issue I found is naming the exported files which contain "illegal" chars, such as the "90/95/99th Percentile..." reports.
Otherwise, I was able to run this script, then import the reports back into the system without any issues.
The exported reports appeared to function/display properly once imported back into the system, and ran.
I hope this works to get you where you need to go.