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My gut feeling is yes:
1. Should be using the limited number of terms as uniquely as possible for each page. I would (try to) limit the meta keywords to eight phrases / twelve words.
2. The search engine is most probably going to list a maximum of two pages, so the effort is wasted anyway.
3. The algo could treat this as word stuffing and so veto the whole site?
Your keywords should come from your title, description, headings and first couple of paragraphs on the page.
You can repeat your main theme phrase in there as most of the time it is mentioned throughout the site. The goal is not have any terms in there that are not mentioned on the page somewhere.
I do that on some sites (Lazy because they are hobby sites). No real problems with the major engines. Doesn't perform at all with some minor ones. Fast, Google, and Ink (I also hear AV) have no problem with this as long as there is spiderable text on the page.
Consistent relevant-themed keywords and phrases throughout the page are best way to bring out the keywords and themes in your site. This means the same or similar phrase or keyword in the title, header, file name, alt text, body text, etc. etc.