The paper-dialog shows up behind drawer-panel when launched from a custom element.
I'm not sure exactly what your requirements are, but I was able to use your dialog element and display it above and not obscured by the panel by simply placing it outside of the
.
Here's what it looks like:
I'm not sure if this is what you want, but to do this, something like the following illustrates a basic example:
Drawer
Item 1
[[_selected]]
Show Dialog
Div