So, thanks for your replies, first of all.
I've found the forum here to be an invaluable source of lifelines when I click myself into a CAD corner somewhow.
In this particular case, I was not, and still am not, clear as to what a near-tangent edge refers to given that the edge I was attempting to radius (apply fillet) is described by two faces that are roughly 90 degrees to each other. Specifically, I still can't see how the highlighted edge is near-tangent to anything as it lies between two surfaces that are basically 90 degrees in angle.
Since this object is on its way to being a door that fits into a "fuselage" opening, I decided to go ahead and cut the 2.5mm clearance from the door object (solid) resulting in exactly the same shape missing 2.5mm along its perimeter.
Once this was done, I am free to apply filets and bevels to the top perimeter of this form all I want and with no errors. This leaves me curious as to what manner of heresy the same geometry just 2.5mm away was committing that would not allow further edge treatment, and what is meant by "near-tangent" in this context.
Since I solved the issue, my curiosity is mostly academic, but I always want to make new mistakes, so any insight is more than appreciated.
I'm afraid an NDA would prevent me sharing the actual file, so I am limited to sharing information and screen shots.
Thanks again.
Colin
Fillet Success