I'd like to be #1 for all of my keywords too... wouldn't we all??? If the client is pushing you follow some of the excellent advice given here and then - push back!
SEO's can NEVER promise #1 results. Aside from fixing some of the aforementioned items as well as starting a blog...in my opinion words are very necessary. Let the client know what the real deal is.
What are you using for spider food if not keyword rich text and content? Why would the spiders want to come back if there is so little to "eat" on the site?
It's just my opinion... and a little common sense.
Good luck to you.