914 fuel pressure drops when going to 40" MAP on the ground, or at lower MAP when climbing

The fuel pressure reading is (or should be) differential pressure with the reference pressure being the airbox pressure. You should see a pressure line running from the fuel pressure sender to the airbox to provide this reference. When measuring differential pressure, the reading you get from the sender (for any stable absolute pressure) will fall as the reference pressure (airbox pressure) increases.  In other words, if the fuel pressure was not being regulated, and was simply remaining constant, your pressure reading would fall as airbox pressure increases.  The differential pressure sender is meant to see the relative pressure that the carburetors see.  

Assuming you have already tried using the aux pump, and that both pumps are working properly, then I would look very carefully at the pressure lines and fittings connecting the fuel pressure regulator to the airbox. These are not typical vacuum lines, they are pressure lines when under boost pressure.  So a vacuum test may not expose a leak that happens under pressure.  I would also want to use an analog differential pressure gauge to verify the fuel pressure sender is working properly, although the engine stumble you are experiencing leads me to believe the fuel pressure problem is real.  But, never assume anything!

(This is a differential probe on a plane which has flown for a while before. I've updated the original post to clear that up.)

Good point about the pressure lines leaking under positive but not under negative pressure. That makes me hopeful the A&P simply missed this nuance.

Problem found: it was a busted airbox pressure line coming from the airbox to the fuel pressure regulator (yellow hose in the screenshot). So the regulator was indeed measuring ambient air pressure.

My engine is plumbed slightly differently from what's shown in MMH_912-914 Series_ED1_R6.pdf, Fig 73-5. The yellow line has no tees, it goes only to the regulator. The blue line, on the other hand, has the tees, unlike in the image. Same air pressures throughout, but a cracked line affects things slightly differently in the two variants.