Relatively new snow/alpine climber so take this with a grain of salt...
Did Sunshine on 6/10-6/11. There was still one gate closed but I didn't think it was 6 miles from where we parked - i thought it was past the Inspiration Point gate but I don't know the road well...anyway, it probly took us around 1.5hrs to get to Cloud Cap from where we parked (stumping along the gravel road in plastic boots - ).
I hadn't done the route before so I don't know when/if the lower crevasses on Eliot typically start to open up but there was nothing significant up to our camp at ~8,400 (4-5 hrs from start). Route conditions were fine the next day despite our late start the next morning (5:30 leaving camp) - although it meant running into some very sloppy snow for about 500 feet of the climb to the ridge - also, our crossing on the upper bergschrund felt pretty unstable - but there were still several options for winding around through the area. It would have been wise to break camp and get moving by 4:00 in my opinion. With temps forecast for this weekend I'd get moving as early as you can possibly drag yourself out of your bag though...
my two cents...good luck on the climb - it's a fun one.
p.s. if you have any specific questions on the route I'm more than happy to give you what beta i can - although anything I have is probly given in more detail in Oregon High...