[mlangsdorf]

Your new version is better, but it still doesn't address some issues:

1) There's no incentive to not attack twice if you have Rapid Strike points, and you usually do. DX 12 HT 12 gives 6 RSP, and that's enough for two rapid swings with a broadsword, the first at skill and the second with a -2 penalty. Normally, that kind of attack is made at -6 for both attacks, and there's a tactical decision involved: more strikes with a lower chance of success, or one strike that is more likely to hit? There's a lot of times when my characters didn't rapid strike under the normal rules, while under your rules they would have almost always performed a rapid strike.
2) It's not clear how Reach 1+ thrusting weapons work with your rules at all.
3) It's not clear how multiple different melee attacks count for Rapid Strike points: a headbut followed by a punch to the stomach followed by a knee to the face is a bit extreme, but it's something that someone might want to do. In normal GURPS, its a combination or a all-out double rapid strike, in your system it consumes some number of RSP but I can't figure it out.
4) You have this term "damage boost" but I'm not sure what it means. The extra magic strength I get from having the Might spell cast on me? The follow-up attack from Flaming Weapon? The bonus damage because my sword has the Puissant enchantment? My per die bonus from Weapon Master? My bonus from Higher Purpose (Giants) when attacking Giants? Normally, all that stuff affects all damage rolls, and I don't have to worry about it. Under your system, some of that stuff might affect only some of my damage rolls, and that's another level of book-keeping.
Come to think of it, can I choose which attack the damage bonus applies to? I might want to have it apply to the last attack in the sequence, under the assumption that my first attack or two will be canceled by my foe's defenses.