Hello! (Sorry, in advance for the long post!

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I recently moved my Betta from his five gallon tank that I bring to college with me into my planted ten gallon tank that I keep at home (About two weeks ago?). The tank is fully cycled, heated to ~79-80. It's filtered, and has one air stone. In the tank I also have three Platys and two African Drawf frogs.
The Betta was in great health before I moved him into the ten gallon tank. Both the ten gallon and five gallon I moved him from are kept at the same temperature and have the same water source, so I did not think it was necessary to do any acclimation.
When I initially moved the Betta into the ten gallon, he was lethargic, hiding, had clamped fins and had some red streaks on both his tail and and anal fin. I assumed that the previous were from both the stress of moving and having new tank mates, as he's never lived with other fish before. He never had any loss of appetite.
After about a week and a half in the tank, he became more active, stopped hiding, and his fins have un-clamped (he's still holding them a little odd though, his tail fin is almost folding over itself?), which I think confirms that he was stressed and adjusting to his new home. But about three days ago, I noticed fin rot setting in and he still has the red streaks (septicemia maybe?). The red streaks at starting from the base of the fins, and fanning out about half the length of his fins. It almost looks like it could be a change in his coloration. I checked my water parameters, which were at 0,0,30. I know that 30 is a tad high for nitrates, but I don't think it's high enough to cause any issues? Anyhow, I immediately did a 30% water change, and have every day since.
I'm assuming that the fin rot was able to set in due to a compromised immune system from the stress of moving and having new tank mates.
But I'm wondering if that is enough stress to cause the fin rot? If it was, are daily water changes going to be enough to nurse him back to health? Do you suggest trying aquarium salt? If so, will I be okay dosing the entire tank with the other fish also? I think that I'll bump up the water changes to 60-70%ish, but with the tank being fully stocked, I don't want to be doing 100% water changes. And what about the red streaks? Is it septicemia? If it is, I have maracyn, maracyn 2, and maracyn-oxy handy, but I would prefer to go antibiotic free if possible.
I do have a 5 gallon, cycled, heated, filtered, spare tank that I can use for quarantine, but I planned on moving my pregnant platy into it within' the next couple days, and using it as a fry tank. I know that I should have a bigger tank for the fry, but it's her first batch of fry, so she'll only have a couple this time around (: If I do have to medicate though, I'll move my Betta into the spare 5 gallon and buy a breeding net or box for the platy.
I really appreciate any advice!