The two-burden style works just fine, IMO, since that hits the key points (the Captain and Army provide strength bonuses, the Axeman becomes fierce and strength +3, and the Polearm blocks wounds). The burdens here are just a tool to get the beatdown to work.
Looking over the revised deck list, I would return
Small Hope and
Raider Bow to four copies (I'd always run four each of
Easterling Captain,
Easterling Polearm,
Raider Bow, and
Small Hope in this kind of build). Can't go wrong with
Small Hope when it starts the party and keeps it going, and also doubles as a strength pump (option to conserve the pool).
Raider Bow floods the pool for the Captain.
Also, a fun card to try is
Bold Men and Grim--who would you like to discard today?