Nope. The choice on this power is part of the hit effect. You choose per target, tho you can only get the Radiant bonus once.
Which affects the keyword, and therefore, affects the Attack: portion of it.
Which means you have to choose by then, and one attack line = one choice.
Not to spit in your weeties but I can't find that definition of an attack/keyword relationship anywhere. Do you have a reference?
I find that hard to believe seeing as the infamous Wintertouched/Lasting Frost combo absolutely relies on it. Also Hellfire Blood.
I could look farther, but when your examples are in the PHB in heroic tier, you need not look any further.
But every instance of 'When you attack with a _______ power, gain a +1 to hit/get combat advantage/shift one square/increase defenses/decrease defenses' absolutely do.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.