I got it done this way:
1) Modified the script by removing the initial commented line, and deleted 'zimbraMailSieveScript: '. So the first line in the script looks like this:
2) Transferred the script to the other server, and assigned the entire output to a variable, like so:
require ["fileinto", "reject", "tag", "flag"];
3) Ran zmprov, enclosing the variable in double quotes:
zmprov ma email@example.com zimbraMailSieveScript "$SIEVEVAR"