They way you have it should be ok. If you are concerned about suspension movement, use an ADDITIONAL strap(s) to pull teh frame down onto the axles.
Straps are much less prone to loosening up compared with chains + binders. Those are better left for securing heavier equipment with less pliable tires or no give(like a bulldozer).
Its up to you regarding strapping the suspension. I never have, and have no issues Depends on your tow rig/trailer, your trail rig's suspension, and your level of driving ability.