But also look, newegg describes it as having 384 shaders so I was almost sure I got the right one.
HI again all, amdmatt, I bought a Sapphire R7 250 2GB and have just installed it and dual graphics is working! I did not uninstall any drivers or anything different since the last card, I simply installed it and booted up and it was recognized in AMD Graphics Settings right away. Dual Graphics option was also available in Additional Settings. The card also now shows as linked. I will run another 3dMark and see how performance is affected. Thanks so much to everyone for helping me solve this issue.
Here is a GPUZ of my current card that works:
A marked improvement in 3dMark on the "Sky Diver" test. I now have a score of 9066 total vs 5368 at best before.