The Ford Muscle Parts Book, page 33, in the "Engine Balance" section talks about adding the 289 HP damper (C5OZ-6516-A) and the HP counterweight (C3OZ-6A360-A) to the 289 2V and 4V engines "...to reduce torsional vibrations to an acceptable level...". There is no mention of changing flywheels or flex plates when adding the HP pieces in this section.
The next section, "Recommended 289 and 302 High Performance Parts", page 33, does mention "using the appropriate flywheel... for either manual or automatic transmission, with teeth count to match the starter gear". Again, no mention of using a specific or different flywheel.
While not a definite answer to your question, it would appear that, at least as for balancing purposes, the HP flywheel and the non HP flywheel are interchangeable, providing the ring gear tooth count match.
Hope this helps.