This is the sweetest set-up for securing cars to wedge trailers that I've ever seen!
I know a lot of guys like to use a ratchet and the 8 foot lasso straps with loop or steel ring, but that type of tie-down was originally designed to secure vehicles to a wheel lift while in tow. A wheel lift has a concave shape that the wheel fits inside,plus a towed vehicle is also secured by tow chains, so the lasso strap or wheel lift strap just keeps the wheel of the vehicle from bouncing out during transport.
If you have a wedge type carhauler, and you want to use wheel strap tie-downs, you have two basic choices if your trailer came with diamond plate decking.
1. Take a plasma cutter and cut holes in the deck so that you can use the wheel straps designed for open car haulers like Cottrell, Boydstun JM Trailer, Delavan, etc. This way, the vehicle is hooked directly into the structure of the trailer, and you're not securing by friction alone.
2. Use a double strap, cinch-style tie-down like the one pictured above. The advantage to a double cinch is that it will not loosen, and it is truly adjustable. The old-school style basket tire harnesses (or wheel bonnets as some call them) are not really one-size-fits-all. The larger basket strap gets hung up on the inside of the tire, and you run the risk of doing damage to brake lines on some low profile cars.
That picture above is of a strap manufactured by Starr Manufacturing. It is model SP-EBSIDESTRAP.