I use the S&S Backpack case. More info here.
https://thorncyclesforum.co.uk/index.php?topic=13407.0My bike is a 590M size.
Once you have successfully packed it, when you unpack it take many photos so that next time you need to pack it, you know exactly what works for you.
I do not recall if I mentioned this earlier, but my Nomad Mk II and the case exceed allowable luggage weights for most or maybe all airlines. I use a luggage scale to make sure I am in compliance. The rear rack will not fit in the case with the bike, the rear rack and some other heavy items are removed from the case to get the weight do an allowable amount. But my tool kit might include a knife, so the toolkit is checked, not carried on.
My past trips, I checked two bags, the S&S Backpack case and another bag because I had enough camping gear that it exceeded carry on luggage volume. So, it was easy for me to put some of the excess weight in the other checked bag.
It is my experience that airlines are much more stringent on weight but a case that is slightly oversize often flies without an oversize charge. I have never seen a ticketing agent pull out any form of measuring tool. My point is that if you get a case that is slightly oversize, you might get lucky. For example Ritchey Break Away cases exceed the commonly used size criteria by a small amount but they rarely incur oversize fees. But I do not know if a Nomad Mk II would fit in a Ritchey case, I use that as an example.
Luggage scales will pay for themselves with one saved overweight fee.