No need to raise the tank. The under-tank clips are a firm fit- the tank sits about 2.5mm off the frame, sometimes a bit differently on each side. I've found I needed to push the clip up firmly- just don't snap it. If the tank is flush on the frame you'll need to loosen the mount to make space.
Just the seat has to be removed to access the front seat mount. The rear strap goes through the slots you see there.