As of DA 1.37.0, a User can edit their TTL value via:
User Level -> DNS Management -> TTL (bottom)

Global method

This method will only work if you temporarily disable per-record TTL values by setting dns_ttl=0 in the directadmin.conf and restarting DA. You can turn it back on after you’re done.  Note that this method sets all records in all zones to the same TTL value.

Also, set your desired default TTL in the directadmin.conf and restart directadmin.

Once both dns_ttl=0 and default_ttl=300 are set, just issue the named rewrite:

cd /usr/local/directadmin
echo "action=rewrite&value=named" >> data/task.queue; ./dataskq d2000

Once done, you can set your dns_ttl=1 and default_ttl=14400 again, and restart directadmin.

By anup