[quote=Aussie
Perhaps set off the heat pack and let it run for a while before you put in into the container ? If you let it run for (say) 2/3 of its rated hours before you seal it in, you may get less pressure.
[/quote]

Dont think that would help.
The idea is to remove all the oxygen, or it at least as much of it as possible.
Since air contains about 20% oxygen, the removal of this will unavoidably reduce the volume of the remaining gas to about 80%.

To avoid a partial vacuum in the container, more air must be admited, and the oxygen in this additional air must also be absorbed.

If the handwarmer is partialy expended before the container is sealed, then it might still have sufficient capacity to absorb all the remaining oxygen, and produce a partial vaccuum as above.
Alternatively the partialy expended handwarmer might be able to only remove part of the oxygen, this would reduce the degree of vaccuum produced, but would be a bit pointless since the object of the exercise is to remove all/as much as possible of the oxygen.