Currents
Using the Canadian Current Atlas, and referencing a 13 ft high tide at Point Atkinson for 6:14 that morning, it looks like a big ebb in the morning followed by a fairly strong flood. For a single point (Juan de Fuca east) it looks like this:

A couple of comments. First, the current atlas shows 2 to 3 kts ebb in Admiralty Inlet at start, 8 - 9 in the morning. Several sources advise that there will be a strong and dangerous tide rip at Point Wilson, extending far into Admiralty Inlet. The advised routes to avoid it are either close in to Point Wilson, or to swing far out towards Whidbey Island. What say the locals?
Second, the strong ebb current flows out from Admiralty Inlet then N and W toward Victoria. A human powered boat would have to make use of that to finish in 24 hours, but with an 8:00 am start I am not able to plot a course to get a boat travelling at 3-4 kt through the water far enough west before the flood. The flood current past Victoria is strong, it would push the boat east again where it would have to wait out the flood. I am not finding a course that gets this kind of boat to Victoria during daylight on June 4. If the cutoff is 24 hrs, that means using the overnight ebb and travelling at night. Has anyone looked at this and do you agree?
Wind
Historical wind data for several points in the strait (Race Rocks, Smith Island and Dungeness Bay Buoy) during June show likely average wind speeds 10 to 20 mph and very high probability of wind direction W to WSW.
http://en.windfinder.com/windstatistics/smith_island
Sail boats that point well in light wind should win big from this, it will be no help to human powered boats.
Rick