The tire mount does not weigh that much, but I agree, loosing it would eliminate about 4" in height and having the wheel directly on the rack would allow me to drop the straps.
The hook idea is great, but I don't put a whole lot of trust in looping it through the mesh, I don't think it's enough to take a really hard impact and fear the tire would fly off. There is a bar going under the tire, but I don't think the placement is good enough for a hook. I did find this product though... only $20 so I'll give it a shot.
http://www.etrailer.com/pc-stm~6280.htm
