It’s grammatically incorrect to place "que ce soit" before a genitive. "Que ce soit" should be followed by appositions to a noun/pronoun which precedes it or by the objects of a verb which precedes it.

J’aime la salade, que ce soit la batavia ou la chicorée.

noun = salade; appositions: batavia, chicorée

J’aime manger, que ce soit de la batavia ou de la chicorée.

verb = manger; objects: batavia, chicorée

If the noun is the indirect object of a verb, then the preposition which follows that verb should be repeated before each object.

J’aime voyager, que ce soit à Rome ou en Italie.

J’aime voyager, que ce soit à vélo ou en bateau.

verb: voyager; prepositions: à, en

But "que ce soit" cannot cut in the middle of a nominal phrase. "la gloire de son intelligence" is a nominal phrase, where "intelligence" is the genitive.

"que ce soit" is followed by the subjects of "soit", which is why there should be no comma after "soit". An inconsistency is that, in practice, "soit" does not agree with the plural subjects after it (it should be " soient" but it never is).

EDIT: Since the subjects are alternatives (separated by "ou"), it may not be inconsistent that the verb ("soit") remain singular.