Apparently the document that I linked (the only I could find about CSS support in JavaFX) only applies to normal JavaFX development and not to the capabilities of the WebView itself (based on webkit).
It does appear that padding-left
and other related layout properties work just fine in the JavaFX WebView. There was something stopping my WebView from loading up all of the CSS (unknown reason). Thus the last few values (which I needed) weren't available for styling the document.
I did some major cleaning and rebuilding of my project as well as wiping of all temp and cache files and this issue 'went away on its own'.
I can see the padding applied properly in the WebView now and I can see it applied in FireBug Lite:
padding-left 22px
I had verified that the rule was in my app.css in the .war file, so GWT was generating and bundling things properly. There appears to have been an issue somewhere on the JavaFX WebView side.