I think of all the ideas presented here - if it would work with your table - I like Jan in VA's idea best.
1) the spring loaded rods are comparatively easy to install - and you would not get gunk on your table from the velcro
2) there would be nothing to catch on the top side or top edge of the table i
3) You would only need one layer of fabric with a rod pocket and hem - and if you bought a non-ravel fabric, you could even skip the hem. (A hem would make the fabric hang better, though.)
4) You could make the "curtain" part as gathered or flat as the fabric called for - the sheerer/lighter the fabric, generally the more fullness is required.
5) You could use as many "panels" as you wanted for openings for easy access to your stuff under the table.