Sorry for not replying soon. I'm bad at navigating this site. I normally just check notifications I get, and the "New Posts" tab, and if I don't see the thread pop back up in the New Posts tab (when I'm online), I normally don't check back on the thread. I've noticed for some reason I sometimes don't get notifications when people quote me (such as the one in post#5).
But anyways, is that last pic of the Betta and his current state of health? If so, he still has his color and doesn't look too bad. I'm not all too familiar with Betta anatomy, but from where I think Betta's bellies/stomachs are (just above ventral fins), he does look a little skinny, but that might just be from him not feeling well enough to eat recently and doesn't exactly indicate internal parasites.
When dealing with sick or stressed fish I usually don't recommend moving them to different tanks as that stress is pretty hard on the already weakened fish. However some cases it is better to do so (prevent infecting others, cheaper to treat in smaller tank, only other option, etc). But if not absolutely necessary, I suggest leaving them in their tanks for better chances of recovery.
Just wondering, the new container the betta is in, is it filtered? I know you are saying you are doing multiple water changes a day. That does have it's benefits, but that too can be more harm than good. It can cause stress from all the chaos of water changes, and the more stressors the fish undergoes, the worse they do. A water change really isn't necessary if the water parameters remain good.
Now more onto the symptoms. Even though from a pic he may look fine, his behavior indicates he is not feeling well. I still can't pin point what exactly is wrong.
This "coughing", does it look like he is choking or trying to spit up/dislodge something in his throat? He might have something stuck in his throat (piece of food, shrimp, gravel, etc). Try and visually inspect.
Or is he just flaring like Bettas do (extending fins and gill plate covers)?
Do the gill tissue looks redder than normal? Do the gill cover protrude constantly?
Is he breathing hard? Gasping at the water surface?
Does he flash a lot? (scratch itself against object, particularly the gill area)
Fish having "convulsions", the only time I hear about that is if they are the verge of dying (suffocating or poisoned), have whirling disease, or some other disease that infects the brain, or from sudden drastic pH or temperature changes (severe shock). I've heard some people say their fish had a "seizure" when the bright lights would turn on.
Or was he just "shimmying"? (means fish fastly wiggling/"swimming" in place)
Just found this vid
https://www.youtube.com/watch?v=2CCLMXmJUk0
It's a Oscar that developed "seizures" from a injury. I guess it's just another possibility. Although your fish only exhibited this behavior after initially becoming sick, so I don't think injury is the cause.
Have you added meds to the tank such as MelaFix?
Do you feed tubifex worms or any live foods?
Those epsom salt baths are worth a shot. He might just be "backed up" internally causing him to not feel well and the epsom salt might help.
Sorry I can't identify what exactly the issue may be. Observe the fish more and try and mention any other symptoms you see.
I would double/triple check ammonia, nitrite, nitrate, pH, GH, KH to make sure those aren't a issue.
I don't see any external signs of disease (besides behavior), so it's probably an internal disease, but I am not certain whether it's bacterial, viral or parasitic.
I normally never use meds unless I know what is wrong, but if the fish is getting worse and you still can't ID the issue, it might be worth attempting to cure whatever disease it might be by using a broad spectrum medication. You could try Seachem Paraguard. If not there are broad spectrum antibiotics. But reply back and I will see if any new info pops up that might help ID what is wrong.
