Happy to confirm the akvavit experiments described below. I used saxby akvavit by Moe distillery in Estonia, Cynar and Dolin rouge with a lemon twist. Excellent combo and still identifiably a negroni.
Tried this last night using equal parts of each ingredient as I didn't realise I only had 30ml of rye left in that bottle. I think that's likely an inferior ratio; the spiciness of the rye was not distinct when stirred down. Just a heads-up in case folks are tempted to try that. (And maybe the ratio should be even higher if it's not 100-proof rye?)
I made it with Cynar instead of Campari for a more herbal, less bitter experience. Just great; the spiciness of the rye goes really well with the artichoke weirdness of the Cynar.
I can vouch for the Cynar variation, it complements the Rye well (with Templeton Rye at least.)
Combining this idea with the Sophisticated Dane below, I can verify that Cynar-Akvavit works very well too - the artichoke weirdness balancing the caraway eccentricity (I'm using Aalborg Akvavit); finished with a dash of Bitter Truth Orange bitters.
I could see this great as a aperitif or after dinner drink. We had it before. Great mix of flavours. Just a slight hint of smoky. Does like to rest and get some additional water. Would recommend giving it a long stir.