Just to update a few things based on some convos from Cryptomancer in the SPL Discord:
There will actually be a 15-minute cool down between removing a card from a conflict and being able to restake it to a conflict, for those that want to level up a card.
The conflict points are awarded on an hourly basis, so if you remove a card to level up and then restake it, you will likely only miss a single 1-hour conflict point award.