@caleb.c thank you for bearing with us through this process and providing extremely detailed responses, it’s greatly appreciated. 
Looking at the APK analyzer at least gives us a (temporary) solution for getting your APK size under the play store limit while we figure out the root cause. For that, we recommend creating one APK per ABI. Based on your APK breakdown, this would reduce the increase in size to between 25MB - 50MB, depending on ABI.
After setting up a project locally and integrating the SDK, I am seeing a total size of 21.6MB for the libs directory (only using one ABI though), so there’s definitely something else going on here. If you take the same steps of deleting and re-integrating the SDK into our sample app, are you still seeing a similar increase in APK size? This step will help greatly narrow down our potential causes.
Let me know if you have any questions. Thanks!