[Koningkrush]

Here is a really condensed rule that should be easy to understand after reading the initial post. I decided to not halve points to avoid confusion, and instead double the cost of anything that would halve points.

Rapid Strike Points = (DX+ST)/4
Alternating strikes with the same limb type (arm to arm, leg to leg, head to head) cost 1 point each. Striking multiple times with the same limb without alternating costs a cumulative extra point.
Double all point costs for weapons with Reach 1 that use swinging to strike, triple for reach 2, and so on.
Any damage boosting effects do not apply to any extra attacks gained by spending Rapid Strike Points.

Maul Test:
Swing 1 costs 3 points, Swing 2 costs 6 points, total cost for two swings in one second would be 9 points, requiring at least 18 ST and DX without using additional options to increase RSP.
Broadsword Kicking: Swing 1 costs 2 points, Kick 1 costs 1 point, Swing 2 costs 4 points (total 7).

It may not be 100% realistic, but it's close to simulating reality and manages to combine Dual Weapon Attack and Rapid Strike into one thing. It would just require a quick note on a character sheet and the point costs would be easy to remember.

I also added the same limb thing because of an example above that causes silly kick swing combos which would be super unbalanced and difficult to pull off. The reason alternating attacks are cheaper are because the impact of one limb allows for force transfer that brings the other limb forward. Shield bashes would be the same as unarmed attacks btw, same as daggers, rocks, really almost anything with C reach.

My final problem is that maybe there are too many points. An average trained fighter swinging with 5 quick alternating jabs in 1 second seems like a bit much, although the skill cost might handle it. It might be best to divide the DX+ST by 5 rather than 4.