North Rim, Tioga Rd, and Crowds

I am planning on doing the Yosemite Falls / Snow Creek loop this spring. It will be a 2 night 3 day hike for me via North Dome, Indian Rock, etc. The deal is I want to do it before Tioga Rd opens, but also don't want to hike across to much snow on the ground. The two time slots available for me are May 11-13 or May 27-29

Based on the current snow pack on the north rim does anyone have suggestions on which time frame might be better? Based on past years it seems to me Tioga Rd. might be opened by May 27 this year.

The later dates will certainly have less snow. But there is a good chance Tioga Road will be open by then.