We used to use button tags years ago and I hated them. We now use Bubblegum soft tags, with the loop to the top of the ear. We don't put the tags in until the lambs are 4 months old. At birth we use tiny metal temporary tags which are rarely lost, and don't tend to tear the ear (we have Hebrideans, Shetlands and we did use these on Soay too, so very small tender ears).
For the damage you have now, use superglue to repair the ears before they heal - we haven't had to try this here, but others say it does work.