I saw that it's possible to download older issues (more than 14 days ago) of the weekly newspapers published by the Südostschweiz group free of charge, so I had a look to see what they publish: mostly regional newspapers for Graubünden and Glarus, partly with official notices from the various communes.
The reason I had looked in the first place was to see whether it was possible to get back issues of La Quotidiana, the Romansh-language daily newspaper published by the group, but you need a subscription for that.
But one of the weekly newspapers (that had free older issues) was nearly all in Romansh: the Fegl Uffizial/Amtsblatt for the Surselva region in the west of Graubünden ("Bündner Oberland" in German). On the one hand, it was exclusively official notices and advertising (and no news or other articles), but on the other hand, it was mostly Romansh (though some communes—presumably those with a majority of German-speakers—issued notices in German or bilingual ones), so I downloaded the most recent available copy anyway and had a look through it.
One thing I noticed was that the names of the days of the week sometimes ended in -dis and sometimes in -gis; I had read that the di/gi spelling thing was a Catholic/Protestant thing in Surselvan, but that didn't seem to be the case any more; rather, it seemed to be a regional thing, with some communes preferring the -d- spelling and some the -g-. (This was especially noticeable in the news of the various parishes, since both Catholic and Protestant ones used both spellings.) I'm guessing this reflects local pronunciation, though it might simply be for hysterical raisins.
And one thing amused me: there was an employment ad for a meinacasa (some kind of director, apparently; at any rate, the list of responsabilities seemed fairly broad) for a nursing institution in Cumbel, and the ad was in Rumansh. And among the desired qualifications, it said, "Enconuschientscha dil lungatg romontsch ei d'avantatg."
An advantage, eh? It seemed to me that if you didn't have a knowledge of the Romansh language, you wouldn't have understood the ad in the first place and known what to apply for and where...