I know this is an old question by now, but i came across this issue myself the other day.
looking at the ICC definitions from this page: https://en.wikipedia.org/wiki/Intraclass_correlation#Calculation_in_software_packages
i have came up with the attached data table and calculating scripts. The ICC is the first Percent of total in each Random coefficients table.
The confidence interval can be derived from the 95% CI to the variance components. Any other confidence range (i.e. 90%) can be produced manually or by changing platform preferences.
I would appreciate it if someone can confirm the calculations and terminology are consistent with the ones presented on Wikipedia.
Perhaps someone can make a GUI add in that will make a nice table with all the different ICC's and their confidence intervals.
All the best,
Ron