I think a cyclocross bike makes the most sense in your quest. IMHO and considering your alternatives they are the most versatile and can change over time more easily than the others if your needs/wants change. I don't understand your limitations though "Compromised" How so? "Gearing limitations" I don't see it.

Let me be an example. Today my cross check is a single speed, a fixed gear or an Alfine 8 speed IGH depending on the day or the weather or the tires I need to ride. Obviously it could have a traditional 2x10 set up as well. So there are really no gearing limitations I use road bars in the Spring/summer/fall, and albatross bars (or flat bars in the past) for winter. It can accomodate skinny tires, medium touring tires Cycolross tires, or 35mm Studded tires. Fenders, and a rack, or not. I ride it to work every day, I ride it all around town, and I've ridden it on 40 mile rides many time. (although I do have a road bike as well). It's fast enough. It's tough enough and it's versatile enough.