I moved three sewing machines with movers this past year - they were moved to storage, stored for six months and then moved cross country to my new home. Really didn't have a choice. For two, I had the original boxes - Janome Horizon and Babylock Ellisimo, so I wasn't too worried about those. Also moved a Handi Quilter Avante for which I had no box. That was the one I was worried about. I packed it with lots of bubble wrap and blankets and made a heavy duty box from a UHaul heavy wardrobe box. Then wrapped the entire box with movers plastic and wrote on the box the orientation for moving (e.g this side up, etc.).
All came through fine.
Since you have hard cases, wrap loose items so they don't bounce around and then wrap, wrap, wrap your machine and put it in a box.
Finally, make sure that you purchase the insurance on your property. We purchased replacement cost insurance for $400, based on the weight of our items and did make a glass claim for $200 which was paid. We had to disclose items that had a value of greater than a certain number of dollars times the weight (Ellisimo) so that they would be fully insured.
Good luck. I am with you, I was worried but all was well.
Cathy