However, you might consider another path- try using only classes without full spellcasting progressions, drawn from all kinds of sources. Where there is a gap, you can modify by changing spell lists and a few other details.
There are ten options for no-magic classes:
Samurai, knight, fighter, barbarian, warblade, rogue, ranger (CW), scout, swashbuckler, marshal.
As I understand it, Song of Ice and Fire has practically no magic - I think even a bard or paladin would be too much. If you don't mind a bit of magic, that opens up:
Swordsage, crusader, monk, dragon shaman, factotum, paladin, paladin (CW), hexblade, sohei, bard, soulknife, psychic warrior and ninja.
I would be reluctant to include Incarnum classes in a low-magic game. Underpowered they may be, but in terms of flavour their magic is very overt and obvious. It's difficult to imagine reflavouring them to be non-magical, whereas that would be quite easy for a psychic warrior (depending on powers chosen) or a soulknife.
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Even so, I would like to echo my suggestion for Reign (Greg Stolze) - which I can see working brilliantly, or Fourth Edition with only martial classes. The new official SIF RPG looks great, but it'll be a while until it's released.
EDIT: I just thought of Warhammer Fantasy Role-Play. Would that work for you?