Go for it. Do a search for bed designs and construction. There are lots of documented approaches. You might want a layer of plastic to keep oil in the asphalt from migrating into the soil. However, if the courts are old, most of the volatiles have probably evaporated.

The courts will be warm in the sun. Mulching the walkways can moderate the heating if necessary.

good point re the leaching. I think though plastic would deteriorate over time (as little as 1 year) Perhaps putting down a gravel layer and then top it off with a landscape fabric to prevent soil from spilling out.

I was thinking of mulching using straws.

BTW - do you know you can create garden beds out of bags of soil which you perforate at the bottom for drainage and cut large holes at the top.

Another method is if you have access to rectagular or square bales of hay. You can group these into large beds, hose down the middle so it starts to rot inside. After a few days add soil on top of the bale and you should be able to plant directly on top. The rotting hay will provide nitrogen to the plants.

you could get more source of information on Mother Earth New magazine. Look for it.