It is thorough testing and reporting like this that keeps me coming back to the Forums on such a regular basis. Thanks for your hard work on this! There are already a few spots I can see may need some fixing in the future, as well as some UI element updates.
If you're able to, could you at least provide us with the numbers that we should be seeing for the weapon specialization skills?
There's no way to really make an informed decision on putting skill points into these skills currently.
Basically it looks like Efficiency can be calculated using this formula: (Efficiency Skill/533)*max(75-Power,0), and Potential simply adds (Potenial Skill*0.05) to all subsystems at all power levels. Efficiency and Potential appear to stack additively. I'll be doing more testing soon, including a work-up on the Performance skills and the resulting confirmation on how these all interact.
Warp Core Efficiency affects all subsystems, but is most effective at low power settings (25) and has no effect for systems set above 70. Here's a list of gains at power settings 50 and 25 (ie a skill rank of 4 will post 53/50 and 31/25):