Going to a lower level skill group is not THAT bad, you don't actually lose the difference in level, they are just not active(no group is effectively lv 0 in that respect, it's just inactive)
Indeed, as contribution don't carry, you might wanna hit that wheel....
Also, it will be 8 hours before you can join the next one, best to leave at end of day and join early next morning. Doing events with your group skill rendered inactive means you will do much worse in dah event.
Also, it will be a week before you can join GNW again, counting from the time you joined the new group. If your group is mostly ok but have an inactive leader so baggies can't be handed out, know that the time it takes to be able to join GNW, thus get reward from it, in a new group is same as the time you have to wait for seniors to impeach the inactive leader and able to hand out the baggies.