Colliding fasteners in electronics retrofit project
From the comments:


  The countersunk screw from beneath is a no-go, unfortunately. There's an assembly paradox here as well, the adaptor has to be installed before the new PCIe device can be attached to it. If the screw head is underneath then you can't get a screwdriver in there. 


We're not beaten yet!



Figure 1. Insert countersink screw from below and add a locknut to leave a male "stud" sticking up from the orange board. A dab of super-glue might help.


The orange board can now be installed first.
The blue module positioned and a nut and optional washer added to the top. If there is a risk of over-flexing the top unit then add a space between the lock-nut and the blue board.