So after much wailing and gnashing of teeth, I found that it was better to make a new group each time you needed to move a large number of machines out of the "[Default Group]" group. This is because there does not seem to be a way to manage the group after you move a single machine to any newly created group.
So in short
1) Create a new group that mirrors the same permissions as the existing one you want to move machines to
2) Use the "edit" option on the far left of the brand new group that only appears when there are no machines in said group
3) Select all machines to move to the new group and use the arrow button to move them
4) Delete the old group that no longer has any machines in it. In turn, if this empties the "[Default Group]" group, this will hide the "[Default Group]" group .
Note: Whenever you have to create a new group to make it easy on yourself I would just add the date to the end of it.
I had to figure this out for myself after LogMeIn support said that moving multiple machines was impossible. Their software has an insanely high number of arbitrary and pointless limitations on it. Especially in the UI department. Their development team is questionable at best.