I know I am going to sound like a nerd on this, but this was the way I figure out imperial scale factors.
Take the denominator and multiple by 12, and then divide it by the numerator.
Remember this from high school
X/Y=A/B
A = XB/Y
B = AY/X
X = AY/B
Y = XB/A
Therefore for ¾”=1’=0”
4x12/3 = 16
So 16 is your scale factor.
I have noticed thou you want to go from ¼”=1’-0” to ¾”=1’-0”.
Therefore
1/4=3/4
There using the equation above (X/Y=A/B), you wish to find X.
X/4=3/4
X= 4x3/4
X=3
But since your drawing is drawn 3x larger then the original detail the alternate units factor would be 1/3 or 0.3333333.
Which is what you had.
Now I could be all full ot it, but that is the way I would have done it.