Don't think, it's possible without applying a patch to the Firefox code.
As far as I can tell, this is the code to render that toolbar: https://searchfox.org/mozilla-central/rev/16652bab8dbb820ce1079263e5a1373de303e656/devtools/client/framework/components/ChromeDebugToolbar.js#99-121
And it's got two class names in there, but applying display: none !important;
to them in userChrome.css doesn't do anything...