This can be done but requires a small bit of coding and you setting names, labels and aliases, none of which can be ignored.
Step 1 - Create a master model
Create the master model that will be the drop down list. Add a string variable and make it a parameter then set the value list to user friendly terms as shown below:
Step 2 - Create your 3 models that you want to execute independently
Use a standard Name and set the Label to be the text that was in the drop down, as shown below:
Step 3 - Add a calculate value tool to master model
Note that the code imports the toolbox then calls the individual model by its Name (so not label),underscore then the toolbox alias (which I had set to myToolBox).
The full python code is as:
if mod == "model 1":
elif mod == "my model 2":