Transfer characters to The Handsome Collection from a different gamertag?

My family all shared the 360 in our living room and there was one account that we all chipped in to pay for gold, so we only played online with that account. Thing is, when I got the Xbox One, it’s mine and I made my own personal gamertag I intend to be using for a while. But I don’t want to lose my characters from BL2 and BLTPS from the family gamertag when I play on my Xbox One. Any way around this or am I screwed?