Sorry for the late reply,
Cheers for all the suggestions!
You know, visitor, I'd never listened to 'Kalinka' before; it's certainly a very good choice! As for broadening the scope of my search, I have, in fact, considered using themes that are not Russian, strictly speaking, like Elena Nazirova's '8 Children pieces' and Chebotaryan's preludes (and I have dug quite a bit into music from the Balkans and the Caucasus) but I think I'd really prefer a 'pure' Russian theme for this.
'Katyusha' and Lyadov's 'Prelude Op.40 No.3' also seem like good picks! As for the Tetris theme suggestion, ronde_des_sylphes, well, yes, I guess it might appear somewhat frivolous ^^, but then again, unless I'm mistaken, it's based on a traditional Russian folk song, 'Коробейники', right? So it could also do the trick...uh, as long as I don't use Sonya Belousova's arrangement, which isn't quite as simple as what I'm looking for.

The Tchaikovsky suggestions is also interesting, ansgarpiano, but I'm not so sure about it, mostly because I'd have to simplify it and that would almost certainly rob it of
a lot of its charm. I'd rather choose a theme that is already more or less simple right from the start.
Shouldn't have closed that vid only after listening to its first 6 secs, brian; those 6 might not be all that amazing, but it gets really good after that.

And generally the melancholy style of Russian folk music fits us very well. Finns are quite different to the other Nordic folks in this respect. We love in minor keys and depressing stories 
Interesting to know, outin! You know, a girl once told me the same about Hungarians and Romanians some years ago. I dunno if it still applies. (?)

Again, cheers for all the suggestions; I still don't settle on a theme (though, like I said, I've already got my eye on some of the ones offered so far), so any further suggestions are still welcome.
Very best,
M.W.