Dipstick pops out

I don't know for sure about that, but if so, maybe you could rig up a cork plug with a tire valve and use a bicycle tire pump with a gauge to check it.
I wonder if the front pump gasket is idiot proof, or if one could inadvertently put the gasket in wrong and cover up the vent passage.

Nope, - a lotta other things wouldn't work if you did.