My great grandmother's name was Mina (not short for anything) and she went by Minnie. I don't think it is too short (but this is coming from someone planning on naming her daughter Etta).
Your classic options for longer names aren't pretty: Guillermina, Maximina, Minerva, Wilhelmina. I wonder if there is a name with the "min" or "mean" sound that you could go with: Jasmin, Yasmine, Clemintine, Carmin, Carmina,