What I do not like is the default LTSpice box symbol for any new model where you do not draw a symbol. That is visually less clear. I like triangles for op amps, BJT symbols for BJTs, and TL431 symbols for TL431.
I agree. Fortunately LTSpice comes with a range of symbols which are easy to reuse by editing the .asc file. Failing that, you can make your own.
A few things I forgot to mention above about the .asc file:
The part number which appears next to the symbol on the schematic is denoted by the following statment:
SYMATTR Value TL431
The name of the model used. It can be different to the part
SYMATTR Value2 TL431_model
You might need to change the first line of the model to reflect the pin order of the symbol.
For example, in the file I posted previously:
.SUBCKT TL431 3 2 1
3, 2 & 1 are the spice nodes used inside the model. The comment above tells you it's cathode, anode, reference.
Their order, depends on the pin order of the symbol. This can be found by opening and right clicking on the pins.
LTSpice\lib\sym\References\RH1009.asy
Another thing which is a bit off-topic is there is also a generic op-amp symbol, [OpAmps] opamp2, which is designed for use with any model. Insert it and right click on opamp2 to change it to the name of the model.
Ok, I see..
Below several models with your schematics.. I have a dozen of various 431 models here (coming from Bordodynov library etc).
Can you post those models (not just images?) or provide a link? Sausage links are tasty but don't help my circuit simulation 
One thing to note is that often models are optimised for different things. In some cases the transient response is important, for others it's temperature stability etc. All models lie to some extent.