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If I understand you correctly, your page is already covering the keywords in the text on the page? Have you checked keyword density with the tool on Search Engine world? If so, did you reach about 10 to 15 percent for your targeted keywords?
Personally, I don't use alt tags to put keywords in there unless the image relates directly to the alt tag. My philosophy is that alt tags are for visually disabled people or for those who turn off images in their browser. If you scatter these keywords all over the place, this would not benefit these visitors. My personal experience tells me it doesn't get you ranked higher if you do use them in alt tags. IMMHO--but I could be very wrong and hopefully one the "older" webmasterworld members will jump in--keywords only contribute to better SE placement when used in context, not by themselves.
I hope this helps a bit...
My philosophy is that alt tags are for visually disabled people or for those who turn off images in their browser.
Can someone be visually disabled so that they can see an alt tag but not an image? Just my flip comment of the day.
I do, however, share your opinion the use of img alt tags should be reserved for only applicable image descriptions and not random keywords lists.