This is really looking like Hole In The Head. It seems that this occurs mostly in Oscars, some Cichlids, and Discus, but rarely Bettas.
The original lesion looks different than most pictures I've seen of HITH, but I believe the recent pitted areas that have developed make a strong argument that this is HITH.
I believe there is a secondary bacterial infection in the first lesion that developed; you can see the inflammation, redness and swelling down the face of the Betta, under the eye and along the mouth area.
Why would your Betta have HITH? Does that ever happen? I found a photo of a Betta with HITH. What could have caused this?
I've read articles that discuss HITH and there are many opinions. Carbon in the filter, nutritional deficiencies, poor water quality, copper in the water, and high nitrate levels in the tank water which in the gut convert to nitrite and cause the fish to develop Brown Blood Disease which slowly decreases oxygenation of the tissues; the tissues on the head of the fish are affected causing the pits to develop.
Here's information on HITH that comes from Aquaticcommunity.com:
"Also known as: Head and Lateral Line Erosion Disease (HLLD or HLLE), Lateral Line Erosion (LLE), Lateral Line Disease (LLD). "
"This disease is especially common in discus fish and Oscar fish and causes large cavities and soars on the head and along the lateral line of the fish. The open wounds caused by hole in the head disease are very distinctive and makes this disease easy to discover and diagnose. If your fish has growing wounds on its head it is likely suffering from hole in the head disease."
"Early signs of this disease are small pits on the head of the fish. This disease often appears simultaneous with a disease called Hexamita and this has lead to these two diseases being frequently confused with each other. Hexamita attacks the intestines of the fish and can often be the cause of the hole in the head disease which has been attributed to nutritional deficiency, The two diseases are however not one and the same."
"Hole in the head disease is believed to be the result of a deficiency of one or several of the following nutrients: Phosphorus, Calcium, Vitamin C and Vitamin D. This deficiency can, as earlier mentioned, be caused by Hexamita and its effect on the digestive system, but it can also be a result of poor water quality, poor diet, or over filtration using chemical filtration."
"Hole in the head disease is often very hard to cure, especially in its later stages, but an improved diet with more vitamins and increasing the water quality by cleaning the tank and performing more frequent water changes might help. It is also recommended to remove any chemical filtration such as active carbon filtration. Improving the diet of the fish can include adding vitamins to the diet, introducing vitamin rich flake food to the diet and removing (or at least cut down on) nutrient poor feeder fish and beef heart from the diet."
From the same site here is information about Hexamita:
"Hexamita is caused by intestinal flagellated protozoa and attacks the digestive system and the lower intestines of infected fish.
The symptoms of this disease are often confused with those of hole in the head diseases as these two diseases usually are present at the same time in a fish. They are however two separate diseases that each needs to be treated. Some fish species are especially prune to Hexamita such as large cichlids and especially Oscar and discus fish."
"The first sign of Hexamita is usually that the faeces become whitish and slimy. During this stage of the development of the disease the fish can still appear to be healthy and eat as usual. As the disease progress the numbers of symptoms will increase and you can often start to see symptoms of hole in the head disease as well. The symptoms of more progressed Hexamita includes the fish becoming darker or even black, the fish start swimming backwards, the head sinks in (becomes thin), weight lossand the fish starting to hide in small corners with its head facing downwards. Hexamita does as earlier mentioned attack the digestive system and can therefore cause nutrient deficiencies in the infected fish. Nutrient deficiency is one of the reasons behind hole in the head disease."
"Since the disease is internal it is necessary to medicate internally. The easiest way to do this is to mix 1% metronidazole in fish food (25g food for one 250mg metronidazole) and feed it to the fish. Feeding sparsely before feeding the medicated food can help guarantee that the fish eats the medicated food. It is also recommended to medicate the water as well by adding 12 mg metronidazole per litre aquarium water to make the treatment more effective. Repeat the water treatment every other day until you have treated the water three times."
Here's a photo of a Betta with HITH:
I applied bold fonts to the points I though especially seemed to be of interest and seem to apply in the case of your Betta.
I know you have been meticulous in keeping his water clean, so water quality is not likely a cause of HITH. You have snails in with him so copper exposure or other metals seem not so likely because your snails are healthy.
Carbon, I don't know if you use that, but this is a suspected cause that is debated anyway.
You feed him a balanced diet, from what I've learned, so I'm thinking he has Hexamita and this has caused the HITH. One thing that struck me was the description of the fish with Hexamita assuming the head down position, which is a strange new behavior your Betta has developed.
Having said all this, in this incredibly long-winded post of mine, I would like to know if you have noticed anything unusual about his feces. Is his poo normal? Have you seen any sliimy white-ish poo?
If he shows no indication that he does have Hexamita, which could be causing the deficiencies that lead to HITH, then we need to look at other factors.
You were concerned about the gravel you are using, and said that it seemed that the problems started after you put that in his tank. The issue of metals in the water; I wonder if there could be levels that are high enough to be causing problems for him, but not high enough to kill the inverts in the tank. We need an invert expert to help us with that.
I wonder if you could get a test kit that tests for metals. You use Prime, I love it and use it, too, and I know Prime is great at detoxifying ammonia and nitrite, and according to the Seachem, nitrate, too. It removes chlorine and chloramine, but I didn't see anything on the bottle I have that mentions removing or neutralizing metals, so It would be really good if you could test the water for copper and other metals.
If we can come to the conclusion that he probably has Hexamita, then I would go ahead and get Metro, and start treating him as directed above.
I'd also add an antibiotic with that to treat the infection that has developed in the lesion on his face, either Furan 2, which I know you can safely use with Metro, or Maracyn, which I'm not sure about, we'd need to check on that. Metro can be safely used with several antibiotics, we'd just need to decide on one that would seem to be the best.
I'm very tired so please forgive any typos, sentence fragments, or grammatical errors. I'm going to go ahead and post this and then check it for errors.
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Thanks. Nah, I'd never take him out of the tank and stress him. This is a fish who gets stressed by simple water changes - enough to hide in the plants for a couple hours afterward. Nope - it's just a GREAT little camera with a "macro" function that allows you to get super close and keep sharpness. That, combined with a really, really laid back, passive betta who just lays on a leaf, completely still (always did), right at the front of the tank, makes for a great photo. 
