The problems of housing Goldfish with Bettas goes beyond their different water temperature preferences. The Goldfish is going to outgrow a tank that size. They have different nutritional needs. Also, they need a highly oxygenated tank.
Sorry.. I had to go for a second and couldn't type a reply..
Well first of all.. Your tank is overstocked..
Goldfish are temperate fish meaning that they are inbetween Coldwater and Tropical.. They should NOT be placed in tropical Climates.. It raises there growth, causes shortened lifespans, and a goldfish in this Tropical Temperature is also a fish that can easily be sickned.. Goldfish should also have high current and surface movement/agitation AND high oxygen levels in there tanks.. Which is unhealthy for a Betta to have.. High surface agitation..goldfish and Bettas also have a different diet.. Goldfish shouldn't be fed mainly carnivorous foods like a Betta should have.. And betts should have Carnivorous AND herbivor diets.. Bettas are carnivores and should NOT eat much plant matter.. Also.. To you sorority.. I personally think you have problems in your sorority.. I had a sorority if 11 and only one had nips on her fins.. And that was the alpha so I ideally think you should add more cover and more females to break the line of sight and disperse aggression.. So my recommendations are to sum them up.. Rehome the Goldfish as soon as you can, buy more plants, silk of live, and get more females to disperse aggression
If you have fancy goldfish they still grow to quite a decent size and ideally should have the whole 29 gallon tank to themselves. They also prefer harder water while bettas do best in water that is on the soft to neutral side of things. IMO goldfish and bettas are too different in care to be compatible tankmates. Even the fancy goldfish that can tolerate a higher temperature range.
Also Hallyx, I had some very young females in a 7 gallon tank and it wasn't long before they outgrew that. This was very densely planted but it just simply wasn't enough room long-term. Ideally I think five to six females in a 10 gallon tank is a good minimum to shoot for. With only three females you are just asking for eventual trouble.
For some reason I thought you had three goldfish, but your goldfish should probably have some more goldfish for company as they are very gregarious fish in my experience.
I've seen a post here where someones teacher put a goldfish and a betta in the same tank and the goldfish actually shredded the bettas fins.. He passed away, despite her efforts. I'm not really a goldfish fan, though, so I'm not sure how common that is to have a goldfish attacking the bettas.
I know this isn't really helping, but I've always been confused about this, haha.
My cousin has a feeder goldfish in her pond that has already reached almost two feet. I think it is about ten or eleven years old and it is HUGEE! I swear that thing could get shot in the face with a shotgun and still not die!