Thermal bridging includes screws
The industry standard for attaching insulation to the outside of a wall is to use screws. Granted, the single point type thermal bridges are less of a problem than things like "girts" but the forces on the screws are greater making non-metal ones difficult to impossible. One option is to make walls that are only held to the building by extending the floor plywood or similarly attached plywood to hold otherwise separate walls for holding the siding or furring strips for the siding. There is something called the "Larson truss" which is basically a less-strong truss by making it out of small pieces of plywood or OSB rather than a continuous piece... it only needs to hold on the siding and maybe the weight of the insulation (but blown-in stuff usually has no incentive to move other than by gravity on the bottom). I want to try and hang a separate wall from the rafters to eliminate all thermal bridging as long as I can glue the insulation to the furring strips or insulated studs like the T-stud brand of new insulated stud company product. Thermal bridging is not the only consideration... I want the additional wall of insulation to move independent to the building so it remains air-tight after an earthquake or foundation shifting or tornado. Cost is also a consideration because those long screws are not cheap.