Yes, the maddened Black Grail calls itself the embodiment of the third magic, which is in fact, not different from the grail. The actual ritual is repeatedly noted to be the Heaven's Feel. So I'd say the core of the Heaven's Feel would in fact, be the embodiment of the Heaven's Feel. Further, this does not help your proposed scaling, as true magic is also not inherently root level in potency or anything currently, its just obtained upon reaching the root.
This also again, does not help you at all. its a materialization of the soul that lets it stay on earth, therefore clearly this means her connection to the root is 1-A?
To go further to debunk these points, the Black Grail herself tells us she wants to consume Saber and co because she needs more servants as fuel to open a path to the root since 5 wasn't enough (sounds just like the grail doesn't it), she is then immediately called the Greater Grail by us and Lord El Melloi. Right before this, the moment she comes out, Zouken notes that its Justeaze, the cup of heaven (the grail), Irisviel says that what she actually is is the grail corrupted by Angra, this is what leads Justeaze to try and say she's the incarnation of the third magic, she then says before the fight, its time for the servants to return to her (the grail summons servants and that's where they go upon dying), when she's destroyed, the servants disappear and its noted that its because the grail, which summoned them, was destroyed, etc
Its very, very clear that Black Iri is in fact, just the greater grail so whatever this weird argument is, just doesn't work upon actually looking at the tail end of the event