How quickly can coral fossilize?
First thing is that the sea-level wasn't necessarily that high when the reef was growing, Hondurus is on the edge of the Caymen Trough Fault Zone and experiences quite high rates of uplift, (relatively speaking, your fingernails actually grow faster but over long periods it builds up). So the Coral reefs you're seeing high and dry could be quite recent in geological terms and laid down at or close to current sea levels.

Live Coral is a thin skin of either algae or tiny animals called polyps over what is essentially already Limestone. The live coating builds up this Limestone in order to 1. protect itself and 2. gain advantageous position as far as sunlight and nutrient rich currents etc... Once the coral builders die, which can happen within minutes of exposure to the air for some species (for others the water just has to get too warm, or too cold), the "skeleton" is already effectively a fossil and pretty well as hard as it's going to get.

Any reef is largely made of Limestone from dead Corals that have either simply been grown over or have been broken, ground down and then the coral sand concreted together because of biological and/or chemical processes to form bulk Limestone in which most or all of the old coralline structure is invisible. The primary mechanism for removing coral structure is actually fish that crush coral chips into sand or even finer grains while feeding on surface dwelling algae. The hardening of these grains into a homogeneous whole is usually a combination of the action of coralline algae creating lime on the grain surfaces that bridges individual grains together and the chemical precipitation of dissolved minerals, particularly calcium carbonate from the grains themselves, into the lime sand beds due to daily fluctuations in water temperature and the associated calcium carbonate solubility shift. As the temperature of the water drops at night more lime can and is dissolved into the sea, during the day this process is reversed by the rising water temperature. This process is ongoing with coral sourced lime being added to the limestone reef steadily all the time it's growing.

In terms of the grey colouration you've observed a lot of that will be land derived sediment that was incorporated into the reef while it was still growing and is the natural colour I would expect from an exposed reef deposit so close to shore. Some of it may also be surface in nature though and the rate at which that will accumulate will depend on the wind, the amount of dust in the environment and the surface porosity of the exposed deposit. The higher the winds, the dust count, and/or the surface porosity the faster that surface will be discoloured by dust. There might be a little bit of chemical staining from water percolation but that's normally in the form of Iron and is yellow, red, or orange in colour, similar to this image from Spain.

Short version not much has actually happened to the reef deposits you're seeing since they were laid down except that as the land has risen they've been taken along for the ride and are now above sea level.

If I missed anything or wasn't clear somewhere along the line give me a shout in the comments and I'll update accordingly.