The strap and leg wrap are great ideas. I wrapped my tripod legs in gaffers tapes before seeing this. I have more background in hockey than tennis, so this was my first thought.
On the strap mod, I think I have a better solution for the bottom attachment. The top attachments previously posted are brilliant, however. My simple solution is to use a small Optech Snoot Boot. It is large enough for all three lags to fit into, and tall enough that the drawstring can close over the top of the leg locks. This keeps the legs together and provides a better top to bottom balance when slung over the shoulder.
The issue I see with the previous methods posted is when you have a tripod with a reversible center column. As this doesn't attach to the center column, it is simpler to change it around.
Thank you
Russell