Seeking a very deep/long reach dual pivot brake caliper. 90 mm drop required
Even a dual-pivot brake probably isn't going to solve the problem you found with a single-pivot brake: after a certain point, those long brake arms are flexing and absorbing the energy you're trying to put into the pads. This is why you generally don't see caliper brakes on fat-tire bikes. I did a quick check, and even Tektro's long-reach calipers aren't long enough for your application.

Cantilever brakes would be the more orthodox solution to this problem. They're widely available and a known quantity.