Interesting post, and one I am going to use as illustrating what I frequently write concerning "compatible" fish. Brandelion, please don't take this the wrong way; there is no real issue here, but your post does prove a point and others can learn too.
In the profile of the Dwarf Gourami, there is the following section [copied verbatim with bold my emphasis]:
Compatibility/Temperament: Both shy and territorial, this fish can be maintained in a larger community aquarium with peaceful and quiet tankmates but not other gourami or active, boisterous fish. Males are territorial with other males. Sometimes other brightly-coloured fish will cause this fish to become aggressive. Should be maintained in sexed pairs only.
Your feeding example perfectly illustrates why. Gourami, like Discus and Angels, need calm companions.
Now having said that, black neons are not going to pose a real threat, so don't worry. It is just a small example of the main point.
As long as the gourami are feeding, all is well. The danger than can sometimes occur in such situations is the sedate fish become too frightened to eat. This is common with Discus and even Angelfish, and many of the quiet characins will also refuse to eat if they feel intimidated or threatened by other fish that are too active or boisterous.
Feed a variety of foods, both flake and sinking. I keep 4 brands of flake and 4 brands of sinking tablets/pellets going at any one time, alternating each day so the fish have something different (both flake and sinking) every day for 4 days before it repeats. And one feeding in the morning is sufficient; except in the case of fry that need more regular nourishment, mature fish can mange without food for days if they are otherwise well fed and healthy. Fish will always appear hungry, or they should; their instinct tells them to eat when food is available since they may not see food again for some time. Don't think you are starving them and keep feeding, that is worse for their health.
Other foods for your fish would be frozen bloodworms, but only as a treat, not regular (every day), maybe 2-3 times a week. Frozen daphnia and shrimp (artemia, brine shrimp) are others. Have a look at our profiles for each species, there are recommendations on appropriate foods for each.