I had my heart set to get a bone sightfishing on the fly in Belize too...and had one hooked but it wrapped me around a dock piling. It's fun to watch them chase the fly though.
But what I learned that day is that they quickly turned off the fly. I tried to get another one to go and the fish would back off the fly. We're not talking about individual fish in a small pod either...we're talking about a school of 50 bones in shallow, calm and gin clear water right by some busy docks.
The thing was...if I switch to my spinning rod and toss a 1/16oz jig head tipped with a shrimp tail, they would swarm all over it. Same school of fish. I tried to switch between fly rod and jig/shrimp and the jig/shrimp always win. Then I tried to cheat and put a chunk of shrimp on the fly just to understand what the factors were. The fish would be interested and they would follow, but they would not hit the fly. Fussy little buggers!
Just in my experience, cudas, jacks and grunts are much less picky. Give them some kind of moving target that looks like food and they will usually hammer it. From the sound of it, you were using a red/white clouser type streamer which mimic a baitfish? If the bones are that fussy, they generally shy away from streamers. Streamers are usually tied larger as well.
My suggestion...go smaller, less flash and more natural. Try maybe #10 with a black bead or dumbell eyes. Sometimes the dumbell eyes are too heavy in calm waters and the fly sink too fast. If you are fishing seagrass areas, the fly may sink out of sight. So tie a few flies with smaller bead eyes and no lead wraps on the hook shank. Try to have them sink slowly so you can get some decent hang time when the fly is visible. But of course, it all depends on current and wind. If it is rougher and blowing, you may need that weight to get the fly deep...or go with an intermediate sink line.
Reefs also tend to hold the species you mentioned. If there are seagrass around, bones generally prefer the seagrass beds. Strangely, Hawaiian bones are mostly reef associated since there is no seagrass bed in Hawaii that I know about.
Tide is a tricky thing...it is so spot dependent. Some areas fish better on moving tides and some better on slack tides. I can't really make suggestions. But what I can tell you is to pay attention to what's happening around you. If you start to see bigger predators on the flats (like big barracuda and sharks), chances are that the bones would start to vacate the flats. Generally though, fish shallower as the tide rise and deeper in channels and troughs are the tide drops. Fish moves up onto the flats to feed as the tide rise and drops back to deeper holding areas as the tide drops. Strangely, during my time in Belize, the bones were found by the docks at slack low tide and they would disappear after. Once the tide rose, I saw stingrays working the seagrass beds. Maybe the little bones know to move out when the water gets deeper.
That's all I know...I'm still pretty new at this as well but that's what I've observed from the little experience I have.
Have fun and share some pictures after! ;-)