persp-mode conflicts with EXWM

[shader]

If I use EXWM and persp mode at the same time, I observe the following bugs:

1. "Second order" dialogs, such as selecting what program to open a download when saving a file with Firefox, do not render. Instead, the background image is displayed as if there is a hole.
2. If a parent window is split, any floating windows it displays will also be split and have an attached window showing another buffer. This can easily be reproduced by attempting to download a file with Firefox.

As yet, I have no idea what the actual root of the problem is.