That will just make a mess.
If you know that the radiator is stock or a Mopar unit it could be that you are being given the wrong radiator cap. The only way the cap would leak as you describe is if there was a great amount of volume of coolant or air leaving the radiator. I would imagine it would take a couple cylinders to make it do that and you would know there was another problem.
what gets my attention is that you say you have driven the van for some time after the initial “puke” and the level does not change. That is basically the way old cooling systems worked. You did not fill the radiator full when cold.
You said you checked the hose to the overflow tank,,,did you check the overflow tanks vent? If that is plugged that could cause your symptoms.