I think we've got a slight misunderstanding going : my point is that nothing you do with the sitemaps will influence the ranking of your pages in the search results, beyond making sure they're indexed properly.
Page priority must have an importance for choosing which page to display in the search results between two pages of the same site. If two pages have the same importance for a particular keyword, for internal links, and all other factors, then page priority has to determine which page will show in the results
Unfortunately, this isn' the case - as you pointed out from the Google advice:
Please note that the priority you assign to a page has no influence on the position of your URLs in a search engine's result pages. Search engines use this information when selecting between URLs on the same site, so you can use this tag to increase the likelihood that your more important pages are present in a search index.
From my understanding of the Google statement, the priority only affects the crawling priority of the site, not the display priority. The reason Google says 'increase the likelihood that your more important pages are present in a search index' is that higher priority pages are crawled first, and thus, indexed first. It doesn't affect the relative order of the pages - because the order of the pages is presumably affected by many things - not in the least of which are keywords, inbound links etc. It wouldn't be possible to assign a higher ranking priority, because the search engine ranking is entirely dependent on which keywords match.
Anyway, that's my interpretation of the information - I'm happy to be proven wrong, but it's my belief that sitemaps are only used to determine which urls are crawled, and in what order. It's the relevancy algorithms that will decide what order the search engine results are returned in.
The best way to ensure that one page is (generally) retuned higher in the search results than another is to ensure that any 'link juice' is passed to the page you want higher. You can do this internally by using 'rel=nofollow' on any links to your less important page. If you have significant external links coming in to your less important page, you could change the url of that page, and then 301 redirect those links to your more important page. This would have the effect of increasing the incoming links to your more important page, and it will rank higher than the less important page over time.