Robert Berger from the horn tells me I had it right the first time. "It should be KAR-i-ta. In Finnish, as well as in Hungarian and Czech, the accent is always on the first syllable." "Saying Zsa Zsa ga- BOR is as wrong as saying Ronald rea- GAN." So it's dactyls. KAR-i-ta MA-ti-la. So does that make it KIGH-uh SA-ree-a-ho for Kaija Saariaho, who is also Finnish? Maybe trochees would work: KIGH-uh SA-ree-AH-ho.
He recommends languagehat.com for this type of thing.
He goes on to say, "Kirsten Flagstad should never be pronounced Flagshtad, as in German. The great lady used to go ballistic when people used the German pronunciation." Wow. This would really be hard to change. It's not really our fault. She is inextricably linked to German repertoire, and by extension German pronunciation. I remember how I laughed the first time I heard shpagetti, but I soon got over it.
"With Russian, the accentuation is so unpredictable it's enough to drive you to distraction. It often falls where you least expect it. It should be vla-DI-mir, ser-GEI, an-DREY, kir-IL, and gen-NA-di rozh-DEST-vensky, mi-kha-IL, Kh is as in Chutzpah, etc. In Polish, the stress is on the next to last syllable." I know the tennis player is actually called Sha-RAP-o-va from watching Russian news.
In French there is no accent to speak of. Just accent everything. DE-BEW-SI. NA-TE-LEE DE-SAY. I never got past French, German and Italian.