Did you ever consider whether this is an issue of post exercise hypos and not an insulin sensitivity problem? Are these lows are occuring only on training days? Changes in overall insulin sensitivity take several days to work off. Do you specifically have a meal following exercise that is designed to restore your glycogen stores?
Being a bit older than you, I train 2-3 days a week and have to raise and lower my basal to adjust for training. I was able to limit my post workout hypos by taking more care to follow up training with a meal and insulin regime focused on restoring depleted glycogen.