Stare tranquillo, pdqaltair! He said "MORE". Our OP does need to get more chain on his nice Fortress, but once that catenary angle is low enough, he'll have a bombproof setup for sand, and a pretty good setup for mud.
As other posters have noted, this is a place where local knowledge can be very helpful.
(I've used a 15lb Fortress on 30' of chain as bower anchor for 30 years in the Chesapeake.)
I'm tranquil. However, there is much misinformation regarding the usefulness of chain, and it is tiresome. I dislike overly broad statements that are traditional, untested, wrong, and mislead new sailors.
I am in the midst of anchor testing for several up-coming articles, and the one thing I know for an absolute fact is that the chain is NEVER near the bottom at full load, there is no catenary in shallow water (what the PO is talking about), and that chain has NO BEARING on ultimate holding power. What chain does do is...
* is cut resistant
* compensates for sloppy setting method by pressing the shank down
* provides shock absorption through catenary in deeper water (over 15 feet) and light winds (less than 20 knots). After that it is straight and has much less effect.
* is chafe resistant
* Moderates the effect of wind direction changes. The wind has to drag the chain around first, slowing the impact of the change. While this effect is small, it can buy enough time for less reliable hooks to rotate.
* it reduces sailing at anchor by boats with this design flaw. A bridle helps too. This can be major, if the hook is getting jerked around.
Scope is what matters on a fluke type anchor, not catenatry. Once the breeze come up, scope is all you've got. Anyone that believe scope exists in shallow water in a storm should put 1000 pounds (not much) on and anchor and watch the chain straighten out. It's really kind of obvious. You will get EXACTLY the same test result with zero chain as with full chain.
Yes, in day in, day out anchoring the reality is different. We use chain to get away with short scope. Bigger boats anchor in more water, so it takes another 5 knots to straighten the chain. We don't need to think about chafe. Chain works better in a windlass. The hook sets faster when we casually drop it. So overall, chain is a good thing. But it aint' holding power; when it really blasts it is about scope, anchor, bottom, and snubber.
(I used Fortress and Danforth anchors around here for 20 years with only 6' of chain. A different part of the world is different, but only 6' is needed for setting. I now use all chain, primarily because I have a windlass.)