Microcap does provide an example circuit called "core" - see my screen shot.
As I understand it, it uses the Jiles Atherton core model. The help topic for it does discuss it a little bit. It is a non linear model.
I'm aware of the examples and of the discussion in the manual and it all seems fine but the divergence from the real-life hardware is what makes me cautious to rely on the sims.
Now, I am not sure if that vendor 3C94 model core you are using is correct- but in theory, it should be able to be modelled correctly.
The manufacturer is Ferroxcube and over the years I've found their datasheets to correspond well with the real-life parts.
The Model program inside MIcrocap lets you build a non linear core model using some data sheet values / curves... so you might want to try that approach also.
I've tried Micro-Cap's core modelling utility a few years back but found it too cumbersome to work with based on the datasheets of some older cores.
The disadvantage of that approach, at least in my case, is that it takes much more time to make a new model based on datasheet and fit the parameters to correspond with the measured values of the physical part, rather than using the Micro-Cap available core models.
The way I see it, if making the sim behave correctly is taking more time and effort than testing the physical parts on the bench, then its advantages are void.
Inside the model are a few things I am unfamiliar with like domain wall pinning constant. who knows if thats set right for the vendor model.. how to even figure it out.
Indeed, that's what's perplexing me as well.
I haven't found the source material that Micro-Cap programmers used as basis for their core models and I haven't find such parameters in the manufacturer's datasheets.
However, they must have based it on something because I suspect they haven't done their own modelling for so many different materials.