If you do not want to do a 301 redirect, then I would suggest not doing a redirect of any kind as 301 is the only one that retains SEO and makes any sense. Your other option is to use a rel=canonical on foowidgetsnews.net that points to foodwidgets.com/contact-form-page.php. That should give foodwidgets.com/contact-form-page.php all of the SEO juice and not cause Google to see foowidgetsnews.net. Then you can make any links on foowidgetsnews.net go to your main domain.
Another option would be to block Google from seeing the entire foowidgetsnews.net domain with the robots.txt file and don't do a redirect like above.
One issue you will run into if you do not do a redirect to your main site from foowidgetsnews.net is that users will bookmark foowidgetsnews.net and go back to it which will mess with your results for the newspaper ad.
However, you should be able to do a 301 redirect using some Google Analytics magic. See this article for more info on how. Doing more research on Google Analytics site should also help you find several different ways to track redirects.
Finally, your best solution is to probably just use a 301 redirect if you can use Google's Analytics to solve your tracking issue. That will keep it super simple.
