This is a set of house rules a friend and I have come to use, after four games. I share them here for the benefit of others, and in the hope of feedback for future development. All are given with a description, and a motivation why.
SEPARATE MORALE TRACKS
Instead of morale being a zero-sum game, both sides count morale separately. Two morale markers are used, one for each house (objective control markers work). Both start at the centre and gradually fall towards the rout space independent of the other. All eliminated units inflict morale loss normally on the side losing the unit (1 for green, 2 for blue, 3 for red), but the side making the kill only gains 1 morale for eliminated red and blue units, and none for eliminated green units. Eliminating a commander causes an additional morale loss and gain of 1, respectively. End of turn morale recovery to morale breaks is ignored. Using a flag token to recover morale increases it by 1, but doesn't affect the opponent's morale. Using a flag token to rally a unit doesn't decrease morale.
This has the effect of making routing the way battles usually end, as the morale of both sides gets progressively worse (unless a side is doing awesomely well and killing a lot more than it loses). It's not only more realistic than zero-sum fight-to-the-end morale, but also provides a much more satisfactory "clock" limiting game length than an arbitrary, fixed turn limit.
CONTINUOUS FIGHTING IN ENGAGEMENTS
If a unit is still active at the end of a turn and is engaged with an enemy, it is allowed to make an attack. If both units in an engagement are active, the side which owns the engagement marker gets to attack first. The attack counts as a normal attack for all purposes, including allowing counterattacks, etc, the only exception being that advance and pursuit isn't possible. Also, if a ranged attack unit has conducted an attack against a target and executed no order after that nor been in melee, it continues firing at the same target until it is either ordered to do something else, gets engaged, or loses its target. If it is active at the end of a turn, it makes a shooting attack at it. If both players have shooters eligible to shoot, the player with initiative conducts all his shooting first.
This is both realistic and gamistic, units ordered to attack a certain target would keep doing it until ordered otherwise, they wouldn't stand idle when the enemy is standing next to them hammering away at them. They have that much of a sense of self-preservation, and unit commanders should at least have that much initiative. Also, it frees a player from having to continuously spam orders at troops already engaged to keep up the attack, and would free them to be used for actual maneuvering, rewarding tactical play rather than making maneuvering a liability that directly decreases the damage output of troops already in combat.
PIKEMEN HAVE COMPULSORY ADVANCE
Pikemen count as having the Advance keyword, but must advance whenever they are able to.
This is simply to cover the consistency gap in not letting pikemen have Advance, despite all other melee infantry (except for super-heavy Lannister heavy infantry) having it. Pikemen if anyone should have it, their combat style effectively based on pushing on and creating immense pressure. There's a reason for why the term "push of pike" was coined. Making the advance compulsory is thus justifiable, and it offsets the benefit they gain from advancing.
HILLS GRANT EASIER STALWART
Instead of limiting the number of dice that can be rolled against it, a unit on a hill attacked from below it needs only be adjacent to one friendly unit (rather than two) to count as stalwart.
This makes troops on a hill enjoy a defensive benefit that's appropriate to their situation (having higher ground should make it easier to hold the line against anyone trying to push you back), instead of inflicting a rather arbitrary penalty that only disfavours some, hard-hitting units instead of everyone.
MINOR HOUSE RULES
An attacker rolling retreat results is allowed to choose whether to inflict a retreat or not. The benefit from Toughness is only applied to the first hit suffered in a turn, not the first hit of every attack. Commanders have "hitpoints" like units, capture requiring a cumulative total of hits equal to capture rating (rather than all in one attack). Jaime's (Kingslayer) ability instead reads as: Whenever you inflict at least one hit on a commander, you inflict an additional hit.
These are all fairly common house rules, already debated lengthily elsewhere so I won't say any more on them.