Pixel,
Cutting it off at 2 generations - Creates Urgency. Doomsday groups have to have urgency to keep membership up.
Lets use 90 year lifespans and 25 year olds getting annointed. If you are 25 in 1914 and get annointed and live to be 90, that would put you dead in 1979.
If another overlapping person gets annointed in 1979 at 25, then he is now 59. Not exactly a "doomsday is tomorrow" equation, but it makes it more urgent than the end could be 180 years (90 + 90) from 1914.
Doomsday in 2094 isn't going to scare anybody into submission.