Sippys are just like bottles and pacifiers, it's all about finding the right one.
DD is EBF too and we have tried 4 different sippy styles and the only one she will take is the strwa style. Have you tried one of those? Playtex makes one that you can squeeze the bottom to help the liquid up the straw while LO is still learning. DD took a few days but she loves it now and she will drink from any normal cup and straw too.