Hi M&d
If you've got an end stop, then you need a rachet strap to pull the front wheel up tight to it (pulling it from East to West if you know what I mean?) This will then stop the scooter moving from side to side. One or two other rachet straps will suffice. We have a bar that goes over the saddle. I connect a rachet strap to that. You need to be careful not to put too much down-force otherwise it can put the suspension of the scooter under compression, which I'm sure doesn't do it much good if it's on the rack for any period of time.
We have travelled right across Europe, over horendous potholed roads and it's not fallen off or damaged any of it's surrounding framework. If you want to see ours, log on to photo's section and look under Biggermac'
regard
bob and Ann