I'm not against fish in cycles. I've done most of the tanks I've kept like you have with feeder fish. Ive cycled with fish food but it's a little messy. Not a huge problem if you do water changes with a gravel vac.The last couple tanks I cycled I used raw shrimp from the grocery store in a mesh bag. That was clean and pretty simple. I haven't tried the pure ammonia yet but the next cycle I start I think I'm gonna give it a shot. Seems very clean and a lot of people here have been successful with it.
As far as your fish getting ill it's probably from the spikes in water parameters as it's cycling. Spikes in nitrites can out right kill a fish in no time. I know when I did fish in cycles I was super anal about it. I would test the water every other day and do frequent water changes. I still sometimes lost fish despite my efforts. Just seemed like a lot of work compared to other means of cycling.
My best advice for a fish in cycle would be to keep that ammonia at .25 ppm
. Do a water change if it goes above that. Do an immediate water change with any reading of nitrites. Nitrates can go up to as high as 80 ppm
while cycling IMO
but it doesn't hurt to keep it at 40 ppm
or less. This seemed to keep the fish alive more often than not.