If you carefully read the help documentation in LTspice, on the topic of diode models, you will see that it says "There are two types of diodes available."
One of them is the usual sophisticated version of the Shockley Diode model. That's the one where you specify things like the emission coefficient and the saturation current. But apparently you don't intend to use that one.
The remaining one is a "region-wise linear model" which basically means it is a piece-wise model. And while these are "light-weight" models, they are also very, very annoying for simulation:
Note the sharp corners? You don't want that!! Sharp corners may drive simulation insane! So you must specify the tanh parameter epsilon to smooth over the curves.
Here's an example using epsilon values to round the corners:
Also, while neither of the above two pictures show it (because the voltage sweep doesn't go far enough), the values for ILimit and RevILimitdo affect the model behavior:
The above two images include how the epsilon parameter rounds over the corners. That's good. You want that.
But what you don't want is the ILimit parameter. It will cause trouble here. And I think you should also not specify the RevILimit parameter. Don't do either. This keeps things simpler for the simulator. If you add them it may cause simulation trouble here. So just avoid them.
I'd recommend modifying the model seen below to fit your needs:
