You can use absolute positioning of your elements and arrange the contents of your xhtml in any order you'd like. There are a few disadvantages but it would accomplish your goal.

But even if it visits the links first, the results are not stored chronologically... each site is worth the placement it has because of things like content and links, not whose page the spider saw first.

I like one expert's advice that I heard once - design for people, not search engines.  If the search engines dictated horizontal versus vertical nav bars then we'd be in a cookie cutter world for sure.

Without knowing how many links you have on your page, or what kind of anchor text you have, trying to give SEO suggestions is iffy.

Right nav works well for SEO. Can't claim that it is better than left nav, but it's no worse. Naturally, this puts the content up higher in the code. It is not uncommon to see navigation in places other than the left side, but it might not be so easy to actually sit up and take notice of it. Visitors don't so much see these things as just use them, unless you hide the stuff so obscurely that they get annoyed. You can see right nav on sites such as Matt Cutts' blog and Google Groups. As for a horizontal bar, if the number of links is only a handful, then they aren't so much "in the way."  I would be more concerned about whether they were redundant. It is doubtful that redundant links help SEO.

I don't think the placement of content higher is as important as the sheer number and repetitiveness of link anchor text. If a lot of your links have the same keyword repeated, then that won't help for SEO. Doing that could eventually begin to verge on over-optimization. A little repetition goes a long way.

Also, if you keep adding links to many pages on every page, thematic relevance could get blurred. You would think that the search engine would know the difference between content and navigation, but it doesn't always differentiate.

When you move nav down in the code, you are trying to soften the influence it has on page relevance. Whether that needs to be done depends on the anchor text  you've got. It wouldn't have the same effect for every site. If your nav link text is either very dense with a keyword, or if it is cluttered with too many unrelated ones, then pushing navigation lower in the code might be helpful, but not so much you could forget all about managing anchor text in general.