At the highest level an estimator like a Kalman filter is estimating an unknown system state based on a model and measurements.
Your sensor has shortcomings such as linear and angular clipping when the shock is too high which is limiting your ability to observe the system and consequently the basic model which assumes that the measurements are proportional are no longer accurate.
If you are unable to improve your measurements (Which you appear to be requiring in this question.) you will need to improve your model. The adaptive filters that you reference are a step in that direction. However in your case you will want to improve your model to be able to handle the saturation of the measurement. Since the acceleration and potentially rates from the gyros are now no longer always known they too will become part of the estimated state. Where the measured values have high confidence when they're being measured directly, but when saturated they will need to be discounted.
And you will then need to extend your model of the system to estimate the evolution of the newly added state model updates which will let your filter update the estimated values of the acceleration and velocities when the sensor is saturated and not reporting accurately.
To build up this model and how it updates, you can either derive/estimate it analytically based on your understanding of the geometric and dynamic constraints on the system. Or you could setup some controlled experiments to empirically develop a model. For your experiments you'll likely want to bring in an external sensor such as a motion capture system to validate and train your model generation. With the model extended to estimate the acceleration and rates while the sensor is saturated you can get an improved result.
Note that your results will vary greatly based on how well you can improve the model update. If you know the situation and can get good ground truth data in all the expected configurations you can possibly get very good data. However if there are a lot more parts of the system which are variable and there's a lot of time when the sensors are saturated this approach will not work as well.
You also are going directly to an online estimator which is required for a live system, however if you're doing crash test reconstruction you could consider using much more complicated model fitting estimation which will batch process afterwards and estimate the values across the period of saturation by taking into account the state of the system before and afterwards. Versus an online filter which only can take into account data collected in the past.
As a side note: This sounds like a moderately complicated issue to resolve as asked and I worry that this is a bit of an X-Y problem where you're presuming an approach to the solution that's sub optimal versus asking for help on the underlying issue. There may be alternative approaches to solving your problem that are easier.