^^^
Not only hotter output, but also the "warble" effect, because too close and the magnetic pull on the string is now influincing the strings vibration pattern.
Just to clarify; we need to distinguish how you're measuring;
Typically, I measure my PU Clearance with the string pressed down at the last fret; I usually start with 7/64" clearance on the E - 6/64s on the G, and adjust "to taste" by ear.
(so assuming your action is set to ~5/64 that would equal 12/64 - or your 3/16 - if I'm "reading' this correctly...
But pressing the string down for this measurement takes (variable) action height out of the equation.
Does your 50s mij have the "raised A" poles?
On the 2 '57 reissues I have (with the "raised A") - I crank the "A" side WAY down to get and even response across strings.
Unless they're purposely high output pickups; I usually don't experience over-driving the input at those clearance heights