From my research last year, Yes April is too soon.
Mid May to mid July seems to be the the period of best riding weather, but you never know till you get there. Many go in Aug and Sept for the fall colors but rain more likely.
We went for 28 day trip leaving Sacramento, Ca on June 16th, 2007.
Several things may affect when you go.
If you want to do the Dempster Hwy to Inuvik in Canada the free ferry system does not start usually till June 1 or so. This is a must do road (more senic than the Dalton Hwy to Deadhorse) and the Eagle Plains Hotel is 250 miles towards Inuvik only a few miles short of the Artic Circle.
If you want to experience 24 hours of daylight, go as close to the Summer Solstice (June 21) as possible. There is a D2D Ralley (Dust to Dawson) in Dawson City, Yukon Territory at that time.
The Fairbanks to Prudohe Bay Dalton Hwy "Haul Road" is 524 miles from the Super 8 Motel to the Prudohe Bay Hotel in Deadhorse. The first 160 miles to the Artic Circle is mostly paved. Coldfoot is half way for food fuel and rooms.
If the weather/road is not to bad and you are comfortable on gravel at high speed (for the record I think the speed limit is 35mph) you can make it to Deadhorse in 10 to 11 hours, even with picture stops. Beware the last 55 miles going into Deadhorse as the gravel is large and sharp and wind across the Tundra can be high. Many come to grief in this section.
I am going again mid May 2009 for a longer stay to see shat I missed the 1st trip. Might go to the King Crab Festival on Kodiak Island in May?
Get a copy of the "Milepost" magizine, pick the events/things you want to do and then set your date for leaving. I like to plan the route, determine the mileage and figure 300 mile per day for traveling. Some days will be longer or shorter but it does not matter as there is plenty of sunlight.
Also go to ADVrider.com and read the Alaska Forum http://www.advrider.com/forums/forumdisplay.php?f=68
for everything you want to know about Alaska.
Click on the Artic Circle link below in my signature line for pics
See you there