I believe I figured it out.
I entered the state tax and Gatlinburg Accommodation Tax as separate fees under MyVR "Property" edit "Rental Fees." I left the state tax as a "tax" under Fee Type. I entered the Gatlinburg Accommodation Tax as "Other" under Fee Type.
On the MyVR Airbnb integrated channel, I set "Include Taxes" to "No". The Gatlinburg Accommodation Tax is Supported and Synced as an "Other" Fee.
If Airbnb decides to collect the Gatlinburg Accommodation Tax, I'll change the "Fee Type" back to tax.
By taking these steps, Airbnb guests are not overcharged with double taxes. And, it doesn't affect inquiries or bookings from other listing sites.