Here you go:

with-lock-ex -q /path/to/lockfile sh -c '
while true; do
    crontab cronfile;
    sleep 60;
done;'

That’s why there’s a crontab rule to load the crontab from a file. Cronception if you will.

Bonus points if your static site sends a 503 with a retry after header.

Unless you’re in Tibet, Xinjiang, or another place observing UTC+8 with a significant offset from local solar time.