Any advice for the "best" time of year would be great.
I also would be interested, as 6 of us from Ontario were thinking about a Yukon trip next year. I did hear the mosquitoes were the size of small birds 
I've asked around the office, among the locals. They say that the bugs start getting bad in June and are at their worst in July or August. Of course those are the best months for heading north! A friend went to Whitehorse one May and found that when it was dry the roads were no problem, but when it rained the unpaved roads ended up like gumbo and the bike looked like it had been repainted in mud brown.
If you pack appropriate bug protection (good repellant, a bug screen for the tent, a wide brimmed hat with a bug cape around the brim etc etc) you will reduce the misery. Or just don't go north at all and stay in my neck of the woods (southern BC) where the bugs are not an issue (except for the splats on the bike) and the roads are the best in North A(hem, hem) for riding. Less of an adventure though, perhaps...?