LTspice supports the Chan core since long ago. Unfortunately, it doesn't support direct coupling with other than linear inductances (i.e. the default inductance). However, as you found out in your searches, there are ways to circumvent this. If it were me, I'd use this link for my needs, but there are other links, as well (and also some examples in the default installation of LTspice).
A few remarks: there is no "specialized" symbol denoted L, that is the general SPICE notation for inductance, ever since 40+ years ago. The parameters are specialized, and this can be checked in the LTspice manual. Even if it is pretty spartan, I highly recommend reading it, at least once, it may save you tons of searches on the net. Also, in the LTspice Yahoo Groups archive and message list there should be more than enough examples to get you started, if the LTwiki link doesn't do it for you.
This is a simpler version to that from the LTwiki, it only accounts for primary/secondary resistances:
Note that I used G sources for their superior convergence over E sources. If you need more than two windings, extending this should be fairly easy, as the Chan core is only used as a "prototype", with one turn; the sources take care of the windings (and anything else that may be added).
The example on the LTwiki, though, should be pretty self-explanatory, I'm afraid that, if you are looking for a simple, "place L, add coupling" sort of transformer, there is no such thing and you're likely be asking for external libraries which will, most probably, have the same arrangement under the hood.
Best Answer
Most SPICE simulators have the ability to monitor operational regimes, telling you when a transistor is in sub-threshold, triode or full active and likewise for current density and over-voltage. If you don't have this in your simpler models you can easily put together macro-models that wrap current monitoring and voltage levels around the device using ideal elements. Of course you can also use .WATCH which aborts the run if parameters are exceeded (using max and mins) and then there is .WCASE which is pretty complex so I'd get my hands dirty in other areas first. Of course you can also run .MC (Monte Carlo) too.