You can technically apply for your non-resident PA License to Carry Firearms in any county. The license will say where it was issued, but that doesn't matter because a license issued from any county is good in any other county (as well as 30ish other states, you may pickup a few extra by having a PA LTCF in addition to TN). Pennsylvania has uniformity/preemption regarding gun laws across the state. The LTCF application form is uniform across the state (the Philly gun permit unit does like to add their own little requirements and BS) as is the $20 fee.

Now, practically speaking, not ever Sheriff's Office will actually process a non-resident. It's BS but is currently the way things shake out. That's why we suggested Berks County as they're known to have a painless issuing process. Whatever one you go to, maybe just call or email ahead to ensure they won't give you any issues when applying.

Another requirement (not sure if actually a statutory requirement) is for the non-resident to have a license/permit in their home state. Obviously you meet this criteria.