The tile files generated by GeoWebCache using gridset 900913 are like: \EPSG_90013_6\02_02\0032_42.png, etc.
How can I configure GeoWebCache that it is generating the files conform slippy map format? That is \6\32\21.png, etc.
There is no easy configuration option to do so but I believe the "backend storage" in geowebcache is pluggable... so it might be possible to write a custom storage backend that uses the same format as slippy map. I would post to the geowebcache-devel list and ask there.