UNIX command line utilities would make most of this work a piece of cake if the various programs can be invoked with options from the command line. (Most questionably, can Finale be directed to start up, run a specific script (with or without arguments), then exit, all from the command line?)

Splitting an ABC file is relatively simple with an awk script; all it has to look for is (1) a header section that may need to be prepended to each tune within the file and (2) lines starting "X:", indicating the start of a new tune. For generic use, the script may also have to filter out plain-text commentary, if not part of a history section. Your multi-tune files may lack either headers or non-ABC commentary, which would simply things even more.

The script could also produce a batch file to run the generated files through the remaining steps. There would then be no need for batch processing facilities in each of these programs, though if available that approach would be more efficient than starting/stopping each program once for each tune file.

There are several freeware packages (for instance, from the GNU consortium) of UNIX utility programs which can be run in Windows command windows. Apple's OS X supports UNIX utilities natively.