I’m running into similar problems.
Macbook Pro 7,1 (13” mid 2010), 2.4 GHz Intel Core 2 Duo, Serial Number 340244X0A**, running OS 10.13.6, so I PRESUME that the firmware has been updated.
Separately purchased from iFixit (2) of: “8GB DDR3 PC3-8500 1066 MHz 204 pin”.
Each one tests good in either slot in combination with a 4MB stick, but…
When tested TOGETHER, the machine is dead (except for the fan).
To repeat: I can get TWELVE MB as 4+8=12, but NOT 16 (8+8).
As of this writing I do not know if I will return one or both, and be satisfied with 8 (4+4) or 12 (8+4).