This isn't a direct answer to your question, but there has been research on a simpler gyro-free and GPS-free absolute attitude determination method based on a trio of 3-axis magnetometers and a trio of 3-axis accelerometers.
Very much like you imagine 4 GNSS sensors, they use a trio of 3-axis magnetometers -- each detecting the 3-axis direction of magnetic north.
They don't need to be at the extremities of the aircraft, just separated in space for sufficient magnetic and rotational accuracy.
The challenge to overcome lies with the fact that "the aircraft environment is very poor for the performance of the magnetometer, with large electromagnetic transients that cannot be calibrated out of the measurements". Their solution is to integrate a trio of accelerometers, and a time-filtered sampling method to reject transient magnetic readings.
They validated with limited test flights, but there is insufficient information to know how it might hold up to less-than-transient magnetic phenomena in the real world due to storms, static charges, etc.
The paper was published by Stanford in 2000...
A gyro-free quaternion-based attitude determination system suitable for implementation using low cost sensors
One future possibility might be to create an attitude detection system which incorporated all three methods (relative "digital" laser-gyro, motion extraction from a trio of accelerometers, vector extraction from a trio of 3-axis magnetometers, and absolute position extraction from four extremity mounted WAAS GNSS sensors), and used each to backup and reject spurious data from the others.
This would not only provide the least likelyhood of inaccurate attitude indication, but it would also provide extensive data on when there is divergence between the different methods.