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This seems like the beginning of a really interesting combat system, that uses weapon reach in a fun and dynamic way, and would actually allow you to simulate the real-world technique of half-swording. Though I will admit I'm not such a big fan of the HP and wounding system, I think the rest of it shows a lot of promise.
An idea I had for adapting this system to tabletop was that you could simply have the ranges associated with certain numbers (like Close (1), Medium (2), Far (3), ect.) and thereby use a d6 or maybe d4 face up to show the current range, thereby having simple and easy way of noting the current fighting range round-by-round or within the round, and you could put them between different figurines to denote their relative combat spacing.
If you're looking for a different name than sword forms, I can suggest a few alternatives: either just calling them forms (if the compound word seems weird to you), or moves or techniques.
As for the forms themselves, I can imagine all kinds of things like full attacks that can do a lot of damage but offer no movement or balance regain, moves that bring your balance back up don't offer much other benefit, techniques that allow you to move in and out of range with a jab in the middle, maybe some passive ability that give you more defense when someone tries to move into a closer range with you, or maybe a different passive ability that lets you make an opportunity attack when someone moves from a certain range to another, or a form that lets you defend better against opportunity attacks.
I think forms should generally require certain weapons. You might be able to substitute weapons of similar reach, but if the move requires a certain form of shield, a knife, two hands, or a free hand, you'll generally need to provide those to do the move unless there a good substitution rules. And maybe secondary weapons or shields might be used in certain steps of the technique.
Also, you should definitely have some sort of unarmed techniques. Some might involve kicks (this would also be a possibility for some armed techniques) and probably revolve around either getting in and out of range really fast, disarming, or occupying the opponent's weapon somehow to avoid strikes since you'd have nothing to parry with.
If you want to lower the amount of dicerolls, you might possibly want to just have a few steps in the move be compared straight against the enemy's defense, though I would personally first consider if it's really necessary to roll the opponent's defense in the first place, rather than just comparing it to a straight defense value (possibly half the dice's max value plus the usual modifiers). Since balance allows these values to fluctuate on a round-by-round basis, it might even be worthwhile to compare straight values without rolls for certain steps.
And those are my thoughts so far without reading up to your second post yet (which may turn out to totally invalidate all my points or something).
EDIT: Looking at Monk12's second post, it seems he did indeed think of a few of the same types of forms as me, though I did come up with some original ones too. I thought of a few more and some other ideas after reading his post:
So I know proposed using Balance as hitpoints, and that could certainly lend to an interesting style, but I think in a fight actually hits should maybe be somewhat rare, as you have to overcome your opponents defenses, one of which should be a passive parry ability that uses the defender's current balance score. The idea should be that, unlike other games where HP represents depleted luck from near-misses and/or loss of stamina to keep up with constantly avoided blows until you get down to the last few that represent actual flesh and blood damage, here every single wound should represent actual physical damage.
I think some moves should allow you to activate some sorts of stances, or whatever you'd want to call them, that would do various things such as boost your defenses or allow you to perform counter-attacks in certain situations. Thinking about it, maybe there should be certain moves that act as combo moves, being able to be used freely upon successfully executing certain other moves, allowing you to not only change stances but alternatively perform a the equivalent of a single step of a regular move as part your turn (it's possible more steps could be included in a combo, but my gut says a single step is probably a good idea since it's an extra thing). Also, some combos, at least maybe stance combos, might be free to execute (since you have to succeed in another move to use them and you can only have one stance active at once (probably)).
Also, some combos might be what I would call default weapon forms, certain moves that can be used by anyone holding a certain weapon at the time. These would, by design, tend to be less useful, powerful, and varied than those provided by actual fighting schools and styles, since they mostly just simulate the general wild flailing of someone who is unfamiliar with a weapon (though there should be some benefit gained from being a generally competent fighter; probably just the general benefits you gain from having a good balance score). Rather than having forms for each weapon, there would probably be different forms for groups of weapons that behave similarly. In addition, there would also be some sort of default unarmed form that could be used by anyone who finds themselves suddenly unarmed in combat and needs to resort to good of fashioned fisticuffs.
Speaking of unarmed combat, my post original spoke of it in a way that implied use against someone with a weapon. While there should be some styles for that, I think most forms of unarmed combat should probably be devoted to defeating other unarmed combatants (and you should probably have to master one of these styles before you're ready to take on dudes with weapons using only your fists).
Oh, and I also thought of another way to keep track of fighting range: do as before, with numbers denoting the range, but instead of using dice, you can add or subtract a number of glass beads or poker chips or some other easily countable thing.
Alright, that's it for now.