Does anyone know how much STR is Equal to one weapon attack?

Actually, the OP needs to take the partial derivative with respect to weapon attack and divide it by the partial derivative with respect to STR to get his desired ratio.

∂(Range) / ∂(W.Atk)
∂(Range) / ∂(STR)

= ∂(STR) / ∂(W.Atk)

∂[c/100*(4*STR+DEX)*(W.Atk)] / ∂(W.Atk)
∂[c/100*(4*STR+DEX)*(W.Atk)] / ∂(STR)

c/100*(4*STR+DEX)
c/100*4*(W.Atk)

(4*STR+DEX)
4*WAtk

Oh look. All the constants drop out anyways.

Oh man, by the time I just found out how to get no. of primary stats per WA, I just got ninja-ed by that.
But anyway, I'll just show again how I solved that using easy yet very different approach.
My idea is that...

Max damage when PS + n = Max damage when WA + 1
where n = no. of primary stat increased (Assume that there's no change in WA and SS)

M - Multiplier
PS - Current primary stats
SS - Current secondary stats
WA - Current weapon attack

M * (4*(PS + n) + SS) * WA/100 = M * (4*PS + SS) * (WA+1)/100
(4*(PS + n) + SS) * WA = (4*PS + SS) * (WA+1)
4*n*WA + (4*PS + SS) * WA = (4*PS + SS) * (WA) + (4*PS + SS)
4*n*WA = 4*PS + SS

n = (4*PS + SS)
(4*WA)

Note: % Damage does not affect calculation for no. of PS per WA at all!!

Q.E.D~~~