I don’t think that you’re going to be able to do this with the time dimension alone. If you had the FY Start and FY End in your data, you could use a formula to calculate the days. But, in your case, I don’t think enough information is available to calculate what you want.
You could get down to the day level if you provide day in the dimension, but the results will be dependant on your data what will show up in the resultant dataset. From below, Jun 01, 2012, might just be the first data point that matches in that year, not the actual fiscal start.