Welcome!
I'm no expert, so take what I say with a grain of salt, but here are my recommendations:
If you want to keep the varieties you have, there are several copper-based anti-fungal sprays that a number of growers on the forum, especially in Florida, use to successfully combat anthracnose and get good crops of mangos. I'm sure there are several threads here you could dig up with product recommendations, and best practices for use. I live in a dry climate, so I don't have any personal experience spraying anti-fungals, but a lot of folks here do.
If you want to experiment with new varieties that should produce without spraying, I would start with varieties from Hawaii and Southeast Asia (Myanmar, Thailand, Indonesia, etc). Those varieties will have been selected in high-humidity environments, likely with a lot of anthracnose pressure.
Hawaiian varieties: Start with Rapoza and ST Maui. Both are excellent mangos, and one of best mangos I ever had was a Rapoza in Kailua-Kona (probably grown on-island). I'd also ask the local mango growers about what does well there, I bet there a lot of good, unnamed varieties nearby with owners who would share a scion or two. For example, there's a guy in Hilo with a YouTube Channel: GreenGardenGuy1. He put out a video about a great rain-proof mango variety he found in Kurtistown. Here's the link:
https://www.youtube.com/watch?v=wMCkKl1AksU. You might see if you can track him down and find out if that variety is being propagated or if scions are available. From the video, it sounds like that mango might be your best bet.
Southeast Asian varieties: I talked to a nursery on Oahu about SE Asian varieties that do well within 1/4 mile of the ocean, and they said people have had luck with Cac (Coc). In a similar veins, you might experiment with varieties like Maha Chanok (chanok, Chanok), Po Pyu Kalay (PPK), and other SE Asian varieties. Try fruitlovers.com (based on the Big Island, I think) for scions if local nurseries don't have any.
Although it's a Florida variety, Fairchild is listed by an old UH Manoa mango research paper as relatively anthracnose resistant. Fruitlovers.com lists Fairchild as an available scion on their website.
Alternatively, I bet there's a thread somewhere on this forum that compiles a list of mango varieties people have found to be anthracnose-resistant. The potential issue here will be scion availability in Hawaii. Not sure how limited the pool is, considering how difficult it is to ship plant material there.
Hope this helps!