I think we are all in agreement that the Elemental Adept (Fire) Feat, Rules as Written, should allow for the potentially increased damage to the radiant damage portion of Flame Strike.
The divide comes for those who consider the Feat not clearly worded, and Rules as Intended to exclude the radiant damage dice.
In reflecting on how other rulings might help us think about this, what comes to my mind are the rulings on Critical hits and “extra damage”.
How does extra damage work for critical hits?
If an exceptionally well-placed sword blow (slashing) is intended to allow a paladin extra damage dice on the subsequent Divine Smite (radiant), that to me is enough to argue that the elemental (fire) feat is intended to apply to the additional radiant damage as well, unless and until something specifically disallowing it is official.