Clark
Are you sure that your straps aren't slipping? I've moved lots of bikes on trailers and in truck beds and have never had a strap come loose if it was tight enough to compress the suspension. With a ratchet strap theres no need to lean on the bike because a good strap will be strong enough to compress the bike. If you are using a cam strap you will have to compress the bike and these straps can slip a lot easier than the ratchet type. You can also modify the strap to attach it to the trailer with a shackle instead of the hooks. That way if it loosens up on a bump it will stay attached and remain tight when the bike stops moving.
Are you sure that your straps aren't slipping? I've moved lots of bikes on trailers and in truck beds and have never had a strap come loose if it was tight enough to compress the suspension. With a ratchet strap theres no need to lean on the bike because a good strap will be strong enough to compress the bike. If you are using a cam strap you will have to compress the bike and these straps can slip a lot easier than the ratchet type. You can also modify the strap to attach it to the trailer with a shackle instead of the hooks. That way if it loosens up on a bump it will stay attached and remain tight when the bike stops moving.