I would try to figure out why the home page is ranking so well for that keyword. There must be something else within your content that's boosting it…it can't be just the one link (which I assume is in your navigation, so don't remove that). I would use the page grader tool to compare the keyword phrase with your home page and find out what is making the page rank for that. If you have already taken out what is making the page rank for the keyword, it may just take time to catch up in the SERPs.
From there, I would continue to improve the content and internal linking around the page that you do want ranked for your keyword. Like stated above, utilizing social media and your blog is a good way to gain some web presence. The press release and back link thing…don't waste your time or energy.
Is the page new? That may also be a factor. Also, is your home page ranking for what you are targeting on there?
