Could use a bit of help with my problem, as I'm somewhat a math-lectic.

PROBLEM: Correcting trajectory for measured barometric pressure and temperature to score first round hits without sighters.
Trajectories are to my understanding calculated according to a standard atmosphere. Change this and the bullet will behave differently and the calculated BC will change.

SO FAR: If barometric correction X temperature correction X original BC = new BC
and
Barometric corr = Standard pressure : measured pressure,
Temp corr = measured Rankin temp : standard Rankin temp

...then I can calculate the deviations (not correctly, but better than not doing it) by working out a new dropchart for the new BC.

I WANT: To find correction factors where I can correct directly from a trajectory chart without going the long way around and making a new one.

Most programs allow you to input environmental variables and generate a new trajectory without changing the BC. The program just changes the air density and speed of sound accordingly.
Try JBM's ballistic site.

Your looking for a way to apply a percentage to your bullets path for a difference in air density?
Like if today's temp is the same, but a front is coming, and today's pressure is 1" of mercury lower. How will that effect my drop today?
Dude, that would be a seriously ugly formula to carry in the field.
However, various common scenarios could be run on a program, and then a list of rough corrections could be made & carried along.

Yes, you all understand the intention with my question correctly. Complicated yes, but satisfactory fun if I can get it working.
True, sighters or several charts will take care of (parts of) the problem.

However, I know hard target interdiction operators correct their MOA on a "fill-in-the-blanks" formula using constants calculated for the various ranges, AND hitting their targets.

I have the data for the Raufoss .50 MP ammunition and I'm familiar with using the form and the calculator, but I don't understand the process of finding the variables that would be valid for other calibers than the .50.

To illustrate:
In the past I calculated a chart for the 600m range I sometimes use, but it was never "quite right" even though very, close. In winter it wasn't all that close.
On a mild winter day I'd get 52 instead of 48 clicks (1/3 MOA scope) for elevation. This I accredited to reduced powder burn rate.
For windage I could get about 41 instead of 37 clicks for windage (almost constant wind from the sea), which I accredited to poor wind calling.
Of course these errors would get larger with range, but 600m is all I have collected data for.
However, when I was taught some neat tricks and borrowed a wind/barometer/termometer, calculated the new BC it all got quite a bit closer.

A calculation could look like:
(stand. pressure: measured press.)x(m. temperature:stand. temp.)x manufacturers calc. BC
(1000:980)x(480,9:517,7)x0,458= 0,433 (BC corrected for pressure (in hPa, works same way for inches Hg if I understand the theory correct) and temperature (simple temperature measurement converted to Rankine).