Kamp/Vlach Sentences Again

Consider the following sentences:

(1) One day, all persons alive now will be dead
(2) Once all persons alive then would be dead

Sentences like (1) and (2) can familiarly be translated using Hans Kamp's doubly indexed N operator, and Frank Vlach's doubly indexed K operator. Kamp's N operator shifts the time of evaluation for the sentence it embeds to the time of reference (which may or may not be the time of speech). Vlach's K operator is used in combination with the N operator. The K operator stores the time introduced by a past tense operator that embeds it, and the N operator is used to retrieve the stored time. (1) and (2) can be analyzed as follows (F is future, and P is past):

(1a) F(for all persons x: (N(Ax) --> Dx))
(2a) P K F (for all persons x: (N(Ax) --> Dx))

However, I think there is a simpler way to translate (1) and (2), for instance (where X is a plural variable):

(1b) For all persons X, F(the Xs do not exist).
(2b) It was the case that (for all persons X, F(the Xs do not exist)).