Moved from Seattle to Williamsburg VA., in 2003. Made the drive 2x.
My recommendation is look for a route that bypasses all the tolls in Illinois, Indiana etc. We took I-90 E to W Montana, dropped down to Denver, I-25??, then I-70 to St Louis then I-64 to Williamsburg. I know, you will have to bite the bullet somewhere to angle up towards Cleveland, but avoid Chicago at all coats.
In 2003 there was no wide spread GPS, and very spotty cell service, especially in the west prairie states. Once you cross the continental divide, it's a very long, boring drive. Got lost at St Louis on both drives. Have seen the Arch from many sides and angles, but remembering the Vacation movie, kept driving for another 100 miles before looking for a hotel.
Have a safe trip and good luck on the new job!