Is this an insane way to mount extruders?

The counter balance mass will only reduce the force in Z.
However in X and Y the issue is inertial due to mass x or y velocity. In these directions the counter weight will not be of benefit and may make it worse as there is a z force due to the cord being at an angle (when not central) that creates inertia with the counter weight = worse than just the carriage on its own.
The advantage you have is by raising the extruders from the carriage the amount of travel is reduced and hence the velocity and inertia goes down.
The only benefit from the counter weight is maintain tension in the cord. The use of the cord is good as it allows for several degrees of freedom of the parts and only a single constraint.
The variation of the bending of the Bowden tubes may cause variations on the feed as you move away from center so it will be interesting to see how linear the prints are.
Good solution to some of the problems.

Yes, it isn't perfect by any means but a compromise between have the mass and physical size envelope of 3 direct extruders, or mounting the extruders on the frame and having excessively long Bowden tubes. For "normal" printing there is very little X Y movement at the extruder mount for a given X Y movement at the hot end. It is only at the extreme corners that it becomes more of an issue. I've some fine tuning to do once I get the printer running. Increasing the distance between the extruders and carriage will reduce the XY movement of the extruders but will mean longer Bowden tubes. I'll have to experiment to find the best compromise.

Plan B (or is it C) might be a system which actively tracks the hot end, rather than being passively dragged around.........