(Side-note: maybe I shouldn't have classified this question as "Best Practices"? I can't figure out how to add an actual answer to the question.)

Thanks to @Randommm for the pointer. I adapted this answer to work with multi-line, sometimes indented contents:

subprocess.call([
    "vim",
    "-c", ":set paste",
    "-c", f':exe "normal i{contents}\\<Esc>"',
    "-c", ":set nopaste",
    filename
])