Sorry, I forgot about that new road. The problem wih both alternative routs are they are pretty complicated. He could be roaming around in some subdivision for hours.
You will need to print out a map, but basically the River place route involves taking a right off 2222 onto River place Blvd and roaming around the golf course to City Park Rd. back to 2222.
The Balcones route involves going further up 620 to Anderson Mill Rd, then to Spicewood Parkway, with a few turns to Spicewood Springs, which connects with 360.
There is mile or so of 2222 that is scary if there is a lot of traffic, but going down Tumbleweed hill at 45 mph is an Austin tradition. Each of the alternative routes adds several miles to the route that might make it difficult to get finished in 3 hours with drive time.
All of these things combine to make an out and back on 360 a better alternative. The hills make the out totally different from the back. Though I have never made it over 40 mph on the descent from Bee Caves.