I found a solution which I'm pretty happy about.
Take a good piece of double-sided velcro (that will bond to itself), about 10-20cm. Get a short, screw with a large, flat head. Put the screw through the middle of the velcro strip, and screw it onto the underside of your table, somewhere out of sight. Rinse, repeat.
Now you have velcro loops that can carry all your wires really neatly, with infinite and easy reconfigurability.
(Initially, I tried gluing / velcroing the velcro strips on. It never lasted, so I went with screws instead. That really works!)