Unfortunately I don't have any tests about it but I think that you should look at the problem with a different perspective. Not on-site SEO could help you, link building would be the key if you don't want to have different spellings on your site. Try to get links with different anchor texts and you should be able to rank for them as well.
I'd personally have the most common version on the site and would try to get links for the second (and third) most frequent keyphrase. Asking a native speaker might help as well.
You may also want to investigate the popularity of a spelling versus the competitiveness. For example, depending on how greate the difference in frequecy is between the most popular spelling and the second most popular spelling, it might be hard to rank high for the most popular spelling, but easy for the second one.