One thing to bear in mind is that you are never going to retain all of the link juice that you've got with the old site when redirecting to the new site.
If I were you, I would really try to clean up the backlink profile of the site as much as possible before doing any sort of redirection. I would argue that you might even be able to salvage the existing site's rankings by doing some rescue work in terms of your link profile.
One very important consideration is that your domain is 10+ years old already, which is in itself a pretty good authority indicator.
My suggestions to you:
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Clean up really spammy links by using a tool such as Open Site Explorer to find and weed out the bad links. Follow whatever process is required to remove some of these links. (Contact the administrator of the site, remove your URL from the directory etc.)
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Help dilute the effect of the spammy links by building new, higher quality backlinks to your site. Diversification is very important. If you have 100 spammy links, but 200 really good links, I don't feel like the Big G will worry too much.
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Check your on-page factors. What sort of content do you have on your site? Are you stuffing keywords everywhere? Are you using unique content, or spun nonsense? Do you have title tags and headings that are both relevant and unique? Are you duplicating any content throughout your site?
The problem, however, with salvaging the site is that, like you say, you're running on a static platform.
If your rankings are really that bad now, perhaps it would be a good idea to start fresh. Just bear in mind that this won't be a quick fix, particularly if you're using a new domain.
If you insist on creating a new site (CMS based) and using the same content, then you'll have to do the redirect to avoid duplicate content issues. I would just take a long, hard look at your content to ensure that it's really worth copying across rather than starting fresh.
Put it this way, I would use the 301 redirect to inform the search engines that the site has been transferred and is under a new domain now. I wouldn't use the 301 redirect to try and salvage much link juice.