That article is a pretty comprehensive walkthrough of one way to do this - perhaps your focus should be to determine where you have gone wrong in the implementation of it?
An alternative (hacky) method would be to put some javscript into the page using a CEWP or modifying the master page that will search for the welcome string and remove it.
Hint - don't search for "Welcome", search for its container which looks a little like this (some attributes stripped out for clarity
<span title="Open Menu">
<div id="zz7_Menu_t" ...
class="ms-SPLink ms-SpLinkButtonInActive" >
<a accesskey="L" id="zz7_Menu" ... href="#" serverclientid="zz7_Menu"
menutokenvalues="MENUCLIENTID=zz7_Menu,
TEMPLATECLIENTID=zz3_ID_PersonalActionMenu">
Welcome UserName
</a>
</div>
</span>
Some links to get you started
http://www.dlocc.com/articles/style-a-page-using-the-content-editor-web-part-and-css/
http://www.cleverworkarounds.com/2008/02/28/more-sharepoint-branding-customisation-using-javascript-part-2/
http://blog.pathtosharepoint.com/2008/08/10/the-content-editor-web-part/