ah, yes, of course that was Firebug already. Somehow mixed this up with the Internet Explorer Dev Tools. Sorry about that...
As I'm out of ideas on why this is not working, we might have to "play our last card": Change the CSS declaration in the original plugin file.
To do this, please edit line 142 in "admin/admin-style.dev.css", to a new and bigger value. Additionally, make the same change in "admin/admin-style.css". The correct place might be harder to find there, as in this minified version everything is in one line. Searching for "180px" might do the trick.
After saving both files, don't forget to clear the browser cache. The textareas should now definitely have increased.
(And just to mention it: This method has the drawback that it has to be repeated after every plugin update.)