I read that you are putting the welsh with long bows which is historically accurate but have you considered the Viking archers ? The Norse in there time were feared just as much for there accuracy with there great ash war bows as they were for there skill with an axe. It was Norse long bowmen who killed the King Edmund of east Anglia ( not very honourably mind you, they tied him to a tree to use as target practice) and most Norse lead battles were started with a hail of arrows from Norse archers, who were just as good with an axe and sword as they were a bow and quite well armoured so they could join the fray when they had shoot all there arrows.
I my self own an ash war bow and there range and power is only just short of one made from yew, but they still have a hell of a thump behind them. A war bow is a bow over the draw weight of 100lbs and so as you can imagine, if you can draw a war bow you can swing even a heavy axe with some ease.