I have hardly ever used equations and never tried linking an external file, so I can't help you with your question as asked. One way around the problem might be to make your hole patterns as an Assembly Feature and check the box that propagates the feature to the parts.
This may take a bit of testing, but keeping in mind equations and properties link via this type of rule:
'variable or dimension name' @ 'config name' @ 'part name'.
Plus if an equation refers to a value that doesnt exist yet, like 'dimension#1' @ 'sketch1' doesnt exist in a new (empty) sketch.
So on a brand new part file, 'post_array' doesnt yet exist. Neither does 'post_sketch' or 'post_plate_sketch'.
By my assumption, when you get the invalid equations, it should error 6 times not 7 (first equation would be valid).
Im pretty new so someone correct me if Im way off, but I think thats whats going on in your case. Took me a while to get my properties friendly between files until I understood equations better.
When you say 'variable or dimension name' @ 'config name' @ 'part name'., do you actually mean "variable@FEATURE NAME@part name" ? I tried the way you wrote it above, and I couldn't get the equation working.
If your variables do not exist yet in your part it will regard them as invalid equations. You can import global variables and assign them to the different dimensions afterwards.