I would recommend that you take a Shinkansen from Echigo Yuzawa to Hamamatsucho and take the Tokyo monorail to Haneda Airport. And then, take an airplane from Haneda Airport to Kansai International Airport.
It will take about 4 hours and 8 minutes from Echigo-Yuzawa to the Airport.
I think it will be difficult to reach the airport by 7:00 a.m. if you leave Echigo Yuzawa in the morning.
So, I would recommend that you leave a day in advance to be safe.
For your information, please the link below.
Have a nice trip in Japan!