Thanks for the replies! I now have a proper ld-musl-i386.path file containing the paths for my libraries. I've unset LD_LIBRARY_PATH and my musl built Python works well.
I'm still configuring musl with --syslibdir=/tmp/musl/lib/. I agree /tmp is a poor choice. But I use three different logins on my dev, test and prod machines and it's not practical to get root access on the test or prod PCs. So /tmp is a good place to at least run experiments.
Any chance I can specify multiple (colon separated?) paths with the --syslibdir option? Or can I make it relative to the current user's home path by starting with "~"?