I would select a few key publications and send them a press release - make sure it's actually newsworthy though. Although many people go online for things, plenty of people still read papers and they still have influence. If you have only sent out a small number of releases, the chances of running into duplicate content issues are not that high - they don't all put their content on the web. Often, they will also re-write the info you supply so that it matches their own style, so it won't be the words you wrote anyway (apart from quotes which will not be changed).
If the content isn't on your own site, it is even less of a problem in terms of duplicate content.
A newspaper article can help with brand awareness and even if readers don't type in a URL to go to your website, they may search for you online instead because they remember your brand.
I wouldn't discount papers quite yet. Try it and if it works, keep going. If the time turns out to be not worth it, invest efforts elsewhere.
You should be able to find out the newsdesk email addresses by going to the website of the publication you are interested in.