Just one thing I'd like to point out. First, the picture here from the trailer.
The reward granted by the elite mark
bill is gil and allied seals. But looking at the topic, we have the following:
Call me crazy, but what I'm getting from this is that the elite marks, which are powerful enemies randomly wandering the realm, yield allied seals and tomestones. The bill, which we receive once per week, is just icing on the cake.
In other words, I don't think there's a once per week restriction on actually finding and defeating these monsters for allied seals.