Last year we got our own domain name and changed web hosting. I also redesigned our website in FrontPage. Our old website is coming up almost exclusively when I search. I've put automatic forwarding on most of the major pages (the old site was thousands of individual pages, so I can't change them all). I know it's been over a month since my last intense attempts to displace our old site with the new one. I'm afraid to take the old one down before the new one appears consistently.

Most of the major search engines consider redirects spam, so they may be hurting you more than helping you. Use them with great caution.

With regard to your website, does the new site mirror the structure of your old site, or is it totally different? When you redesigned your site, did you rename your pages? If your new site resides on the same server as your old site, you should be able to take advantage of the old pages sitting on the server. If you are using a totally different domain name, it is definitely possible to point your old domain to your new. This way, your old pages will continue to drive traffic to your new site versus being a dead link on the search engines should you decide to remove the old pages from your web server. I recommend leaving the old pages up. It takes a long time to build a presence in the search engines. The goal is getting people to your site. If they come in on an old page, as long as it links to your new site, it should be transparent to your visitors.