The advantage of specifically initiated close combat is that it makes the issue of who is the attacker and who is the defender obvious for any given combat.
Anyway, my tinkering took Bob's comments into account, and today I decided to set up and refight a historical action, to see how it played out. I chose the 1642 Battle of Southam, as there's a convenient scenario online and the forces are modest.
Here's the battlefield, with the Parliamentarians at the top and the Royalists at the bottom. I compressed the battlefield a little. The river along the bottom is impassable aside from at the bridge. I allowed a unit to retreat across the bridge to a bonus square beyond, and then return to the fight from there. But it never became an issue. The hills covered up the grid, but it's not hard to infer where it is. The fields were just for garnish and had no effect on play.
Parliament had: 1 x Commander, 2 x Average Pike & Shot, 1 x Raw Pike & Shot, 1 x Average Trotter, 1 x Raw Trotter, 1 x Raw Artillery. I gave 1 of the Average Pike & Shot an extra hit because it seemed to be bigger than the other units in the battle.
The Royalists had: 1 x Commander, 1 x Average Pike & Shot, 1 x Raw Dragoons, 2 x Raw Gallopers, 1 x Average Gallopers, 1 x Elite Gallopers, 1 x Raw Artillery.
As a summary, the rules are based on the Ancients set in 'Developing the Portable Wargame'. Pike & Shot are Heavy Infantry with a range of 2 and who give a penalty to cavalry attacking them. Trotters are cavalry who receive no bonus in close combat, but who can shoot at an adjacent unit. Gallopers are close-combat only, but get a +1 when attacking and must pursue. Those are the main changes.
Here's a view from behind the Royalist line.
And across the battlefield. I went for a conventional deployment with foot in the centre and horse on the flanks.
Parliament advanced cautiously at the start, whilst the artillery traded shots with each other.
The Royalists countered with a cavalry charge, which quickly drove back and damaged the outclassed Parliamentarian horse.
The Royalist foot also edged forward so that it could fire.
Pistol fire drove back some Royalist horse.
In the centre, Parliamentarian foot advanced against the dragoons on the Royalist right, but couldn't hit them.
The Royalist horse outflanked the Parliamentarian trotters.
They ran, and the horse fell onto the flank of the Parliamentarian foot.
The Royalist horse had turned the other flank as well.
In the centre the Royalist dragoons saw off the foot attacking them.
The Royalist artillery destroyed its Parliamentarian opposite number.
Both armies had an Exhaustion Point of 9, but rather than count accumulated hits, I only counted lost units. Otherwise Parliament would have ceased fighting on turn 2, having accumulated lots of hits all along the line. The loss of their artillery, however, saw them reach their Exhaustion Point.
The main unit of Parliamentarian foot was surrounded and, after a tough fight, destroyed. This took their commander off the field as well.
This left Parliament fighting a desperate battle for survival with a unit of trotters and one of foot, both of which had taken a few hits.
Eventually only the trotters were left, so I ended the battle.
The Royalists seemed to have picked up an easy win, with their cavalry superiority offsetting Parliament's superiority in foot. I set it up again, but this time added the walls that are present on the scenario map. These are impassable to horse (I decided), so closed the battlefield down to a width of six squares. Whilst a flanking move was possible along them, I thought that limiting the battlefield like this would reduce the scope for sweeping moves by the Royalists.
Parliament went for a more aggressive attack, launching the trotters straight at the Royalist horse instead of holding back to shoot. The aim was to lock the Royalist horse in place so that Parliament's foot could come up quickly and get stuck in.
It didn't really work. Once again the Royalist horse quickly overwhelmed their opposite numbers.
They then turned on the flanks of the advancing Parliamentarian foot.
Parliament put up a good fight, but they were in trouble very quickly.
Once again the dragoons held in the centre.
Parliament's foot found itself attacked from all sides by marauding Royalist horse. They quickly reached their Exhaustion point.
This was their finest moment, though. Assailed from all sides, this unit of foot won two consecutive combats fighting to its flank/rear, in both cases destroying Royalist horse that was on its last hit. This actually pushed the Royalists to their Exhaustion Point.
In both games it was obvious Parliament was outclassed. The Royalist horse is good, but I don't think that their close combat +1 was excessive; they only get it if they initiate the combat, unlike pike & shot who get it in all cases. Their greater strength lay in the ability to make flank attacks. The trotters seemed weak by comparison. I may give them a +1 in defence, as well as their shooting capability. In terms of the scenario, looking at the numbers Parliament should have four times the numbers of the Royalists, so maybe instead of giving one of their bases an extra hit, I might give them an extra unit instead. This should pad out their line a little, making them harder to outflank, as well as increasing their Exhaustion Point. But that's for another day.
Update: I tried the scenario again with Trotters getting a close-combat +1 in defence and with Parliament having an extra Pike & Shot unit, and it was a much closer game. Parliament reached its Exhaustion point first again, it's true, but the Royalist horse was shattered with one unit lost and a couple on their last hit. It was a much more satisfying game.