Well done, you're going the right way. And to address a couple of things said earlier.
The reason some of your fish are still alive is because they're biological creatures. Although the cycling process is probably toxic to all fish, different fish have different tolerances. And even within a species their will be some variation. So you'd expect to lose practically 100% of the neons you have as they go through a fish in cycle. But because there will be some variation if some survive it's because they had a higher tolerance.
However... this brings me to a point Guppi mentioned. I don't like the term 'hardy'. It's fair to point out that certain fish don't do well in non matured tanks... but I don't like any fish being termed hardy. Ie. fish shops still sell danios to cycle tanks cause they're 'hardy' fish. Yes they are more likely to get through fish in cycle, however it is handled, than neons would. But just because they can take more poisoning doesn't make it ok and I feel the term 'hardy' is used to sort of condone it. The cycling process still often gives them a much much reduced lifespan.
Also, bettas aren't considered 'weak' or bad cycling fish. Not that I would consider any fish a good cycling fish cause I'm a firm fishless cycling fan.
However the first problem, ammonia, primarily causes damage to the gills lowering the efficiency of O2/CO2 uptake/removal. Bettas take their air from the surface and process it in their labyrinth organ. They do suffer from ammonia burns to the fins (black edges) and other complications if the ammonia level continues to rise (which could be what happened here considering how many fish were added). But more often than not they get through fish in cycles fine.
I'm not neccesarily disagreeing with Guppi32011 here, I just wanted to expand and explain a couple of points.