For Attempt #1, the “not found” mtxrun has 0755 permissions. I think the error is some odd side-effect of trying to run a glibc binary on a musl system.
But I realized that I was confused by the installation instructions in Attempt #1. The instructions should say, “2. `wget [URL]`” to indicate to the installing user that “[URL]” must be manually specified. Instead the instructions currently provide a URL which happens to be wrong for my system, thus leading to the above problem. I should have read more closely, to see that it says the URL is supposed to be replaced.
However, correcting for that oversight leads me to Attempt #2, which still fails as described in my first email.
Has anyone successfully installed ConTeXt on Alpine?