Pyura DNA extraction
With reference to your gel photo, the genomic DNA (in the three Pyura sample lanes) does not look badly degraded.  If the size marker is 1 Kb ladder, then the majority of the DNA is of high molecular size. During extraction it is common for high molecular weight DNA to become "sheared" to some degree (mechanically broken into smaller fragments). This can appear as the faint downward smear. The lanes may be somewhat over loaded as well. You can try to use more gentle extraction technique and see if it helps to your satisfaction. Any of those you mention will work.

Badly degraded genomic DNA would appear as a more intense "smear" near the lower portion of the 1 Kb size standard.