I don't think your substrate is killing them. That is mostly a myth. Yes, you can have issues in some circumstances with too much bacteria built up in your substrate (be it sand OR gravel). No part of this looks like substrate death IMO. The deformation and rising to the top are indicative of a much greater issue than some barbel wear. It can indeed potentially be a bacterial infection. But, since it took the cories that quickly, I would be inclined to think that it is something they came in with. Stuff like that has the potential to pass to other fish, but of course that depends on a variety of other factors including the strength of the immune system of your other fish.
For what it is worth, when you get bad stock, the time line for their demise is generally in the span of about 3ish months after you get them. It is not necessarily instantaneous. Death a week after purchase in a clean tank with solid parameters usually screams "bad stock" to me.
Asking your water change schedule is certainly a valid point. IME, usually people have a pretty decent pwc schedule though to maintain parameters like the ones mentioned. If not enough water is being changed, the parameters typically reflect it and the nitrates stay up at more like 40ppm. Though, asking the specifics is never a bad thing either.
At the end of the day, you do the best you can, and sometimes fish die and then you feel bad. Since you have had so many deaths, I would always suggest doing one or more very large pwc ( can be on consecutive days) with a very thorough gravel vac to try and make sure anything icky that may have gotten into your water has been removed. If you want to try cories again, I would try a different store. If you are concerned about your gravel harboring too much gunk, then vacuum the crap out of it (figuratively and literally).
If you are concerned and would rather not try cories again right now, then do what you are comfortable with. Personally, I like gravel. But, if you want sand, look into play sand or some other cheap option. It is way cheaper than gravel. Pet store sand is quite pricey, but there are other options.
Also, if you have a tank that can be set up as a quarantine tank, that would be most helpful.