Planning riding OTET in late August-early September, and have done a fair bit of research as well as local riding on the north end.
While my plans for the tour don't include the RNRHOF (been there a zillion times since I'm from Cleveland), I think the best route there is as follows (starting from the Towpath):
https://goo.gl/maps/BRPSC3rn75uSghvP9
In this scenario, you'd cross I-90 on the West 11th pedestrian bridge and just ride through the flats to downtown CLE. You'll have a climb out of the flats up Saint Clair, but nothing you couldn't handle if you survived the Amish country stretch.