I would also watch the swordtails. They are known to be a bit nippy from what I've read (and also what I've seen when I kept them in my first aquariums years ago), and I'm sure your bettas would not appreciate that very much. I think the males are mainly the nippers (and they are known to be aggressive with other males, so you wouldn't probably want to have many males in the first place), so going with females may get you a more peaceful setup, but really it's up to the temperament of the individual fish as well. It's possible your girls may end up being more aggressive and they may not do well in a community setting at all just as it's possible you'll get fin nippers in other species.
Really you sort of have to experiment, but make sure you have a plan and somewhere to remove fish to if it doesn't work out seeing there is no real "rule" as to what gets along. There are trends that are true 95% of the time, but with all living things there will always be an individual out there that breaks the trend.
You may have more luck with the platies, but the cories would probably do best seeing they are bottom dwellers and will normally stay out of a betta's typical "domain." Of course, I have never kept bettas in a community setting like that, so I'm sure there are some trends I'm missing. The only time I kept a betta with other fish was a male with a few tetras and a pleco, and that was years ago when I was first starting out (and decided I wanted a betta vase, only to find out later my boy wasn't doing so well in it and my only other option was to plop him in my little community), and I don't really remember how things worked out.