I've ridden most of your proposed routes in June and actually the mosquitoes weren't terrible.
The bigger problem was having to wait until the 2 ferries were running on the Dempster as the road
is closed until the rivers stabilize after 'ice out.' You want to do that hwy as soon as possible to avoid the bugs.
The other big and frustrating problem is the quagmire of sticky mud the Dempster turns into if it rains, especially
the top third. Again though, when traveling early, you'll find many of the smaller facilities still closed.
When traveling the Alcan in June you should be aware that both grizzlies and black bears are just coming out of
hibernation and are hungry as well as grumpy. If you get good weather (which is quite likely in June) it's
a great ride, just be prepared for limited services and choose your campsites carefully. Also be aware of poisonous
gases when picking a campsite that accumulate in low lying spots near the oil fields in eastern BC.