I'm one of the lucky testers of 23andme's new Ancestry Finder, which I think is bearing out the theory you elucidated. At 5cM, using only old world countries, I'm 1.4% UK, .7 Ireland, .2 Spain, .2 Netherlands, and .2 Italy. Adding colonies: 26.1% US, .5 Canada, .2 New Zealand, .2 Australia.
It's all based on survey results in which fellow 23andme'ers self identified their ancestry, parents, grandparents...so it's not as scientific. But what I find interesting is that I should share so highly with others in the US and so poorly with the other colonies. This is not what I expected, per se, but makes sense given what you outlined would happen using the Swede/Italian/Russian admixture over time. I'm curious to see if people from the other colonies get the same results, such that Canadians get the same lop-sided results with other Canadians for example. The tool has not been released yet, so time will tell.
The joke in the US has been if you go to Europe you should say you're from Canada to avoid European derision of the US. Maybe that wouldn't work---my genetics (phenotype from genotype) may give me away! Can Europeans pick out Americans just by looking at them (aside from mannerisms/dress)?