I was able to copy my keys and config to nutomic/files/ and use my keys when when thigns go wrong and do a fresh install. Now I see that that idea does not seem to work. it keeps trying to recreate new keys even when I have put my previous keys in place. This leads me to think that somethings has changed inST for Android in last couple versions.
When you choose “Export settings” in “Settings”, it should save cert.pem, key.pem and config.xml to something like storage/sdcard0 (at least for me it does). When put your files there and click “Import settings” it should use these files, although I didn’t try this one.
It is also possible to read/write the keys and config in the app’s data folder (/data/data/com.nutomic.syncthingandroid/files/) with root, but that shouldn’t be necessary any more.