If you do use a sparrow, make sure you have it well secured so that you can control his carrying attempt. I know how this can go, they are quite adept at trying to carry off small stuff, like chunks of meat that they steal off the lure, etc.. Most Accipiters do not want to eat in the open, so they always try to take it to thicker cover, even if they have to drag it there. Its just their survival strategy...get out of the view of other larger raptors that want to pirate their food.
And yes, using larger prey is helpful in curbing the desire to carry. But, it doesn't really change the fact that when they catch something smaller that they will still attempt to carry it. I would target prey that is just beyond their ability to carry well. So Mynahs might be the best choice long term. But initially, until he/she is feeling successful, the first few should be something not too tough to handle.