In the past I've seen a number products that can be laid down before putting in the turf. Using the hardware cloth might not be a long-term solution. Even though it's galvanized, I think that being in a moist environment all the time, it will not last that long, maybe 2-3 years.
What's needed is something that will spread out the weight of the vehicle and last for years to come.
PermaTURF plastic pavers
Roll Out plastic fencing -
https://www.fullsource.com/resinet-s...l6XRoCvnnw_wcB
Also, there's Geogrid Universal, Soil Stabilization Grid 6' x 50'. You could cut this is 3' strips.
http://www.agriculturesolutions.com/...t-IBoCQeLw_wcB