I have also have some interest in using a user defined 'uncertain type' - one that includes not just a value but also an uncertainty - a sort of 'plus or minus' (and calculation operators propagate the uncertainties).
Can you see any reason why it would not work with a user-defined type like that?
(Leaving aside downsides like much longer compute time).
As long as the (+,+=,...) are defined everything should work. You can have a look at the solar system example where a point type is defined.
But perhaps there are other better ways of estimating uncertainties of the final result?
Hmm, what people usually do it to integrate the linear perturbations of the systems. In this way one gets a huge amount of informations about the dynamics, i.e. is it chaotic, regular, dissipative... ( have a look for Lyapunov exponents for example). Any perturbation will converge quickly to the most unstable direction. If you like I can give you an example how to integrate the linear perturbations. Best regards, Karsten